As far as I understand, pork was originally banned from consumption since it was hard to maintain a clean enviroment for pigs in a desert climate (as summarized in the Wikipedia).
Since nowadays there is a much better understanding of how diseases transmit and modern technology for keeping animals healthy and clean, is it possible that pork would be allowed for consumption sometime in the future?
No. Pigs are singled out by the Torah (Leviticus 11:7) as one of the unkosher animals that have a single kosher sign (they have split hooves but don't chew their cud), and as such, are Biblically prohibited. A Biblical prohibition cannot be overturned (Rambam's Laws of Foundations of the Torah 9:1).
(According to some,) the kashrut laws were not instated for health reasons -- they are laws given by God to separate us from the nations.
There is an Agadic opinion brought in Or Hachaim in parshas Shmini 11:7 that after the arrival of Moshiach, the pig will begin to chew its cud, and will at that point be Kosher.* Until that day, the Torah clearly gave two signs which we base our dietary laws upon which cannot be ignored.
Whether or not Rabbis throughout the ages have tried to make keeping Mitzvos more palatable by giving reasons for them or showing how good it is for us to keep them doesn't detract from the fact that they are statutes of the King.
Specifically concerning pig, while the Ramban explained a good point of not eating it was the diseases associated with it, it should be noted that Rambam (Moreh Nevuchim 3:48) singled the pig (and fats) out as the one nonkosher animal which people claimed could not be explain through scientific reasons why it should not be allowed. He went on to explain his opinion of why it is unhealthy.
The Chinuch in mitzvah 73 gives a general overview of Hashem's dietary laws which he himself references in mitzvah #154 concerning unclean animals, he says 'And if there are any reasons for the dietary laws which are unknown to us or those knowledgeable in the health field, do not wonder about them, for the true Healer that Werner us against them is smarter than us, and smarter than the doctors'.
Rashi listed pig as one of chukim, laws who's reasons are not known and our evil inclination and nonjew tell us make no sense, and therefore the Torah gave a special admonition with the words 'I am Hashem', see parshas Acharei Mos 18:4.
See also Rashi in parshas Kodshim 20:26 'do not say I am disgusted com pig, rather say I would like it but my Father in heaven has prohibited me'.
*An interesting idea based on this is found in Chassam Soffer in Toras Moshe parshas Re'eh pg 33 and in Chassam Sofer al HaTorah parshas Shmini pg 101. He says according to the midrashim that pig will become kosher in the future, pig meat today which gets mixed into kosher should not be battul being that it is a davar sheyeish lo matirin, see Shulchan Aruch Yoreh Deah siman 102. He says this is not true. It's not that a mitzvah will be annulled and pig flesh will suddenly become allowed, but rather at that future time pigs will become ruminating animals and by that fact will from then on be kosher. But the flesh of any pig which had died before then will remain nonkosher, and as such pig meat is not a davar sheyeish lo mattirin. Sorry for jargon.
No, pigs will not be kosher food, not even when pigs learn to fly -- well, at least not until the Messiah comes or science finds a way to change the pig from a pig into something else a bit different.
The Torah prohibits animals that can be eaten based on physical characteristics. Leviticus 11:1-32. A kosher animal among mammals must have a cloven hoof and chew its cud. Lev. 11:3. The Torah goes on to give us examples: a camel, a badger, and a hare are forbidden because they chew their cuds, but do not have a cloven hooves. Lev. 11:4-6. The swine is given as the opposite case because it has a parted hoof but does not chew its cud. Lev. 11:7. The Torah gives us no other reason, certainly no health reasons. And I am unaware of any health reasons that make it unsafe to eat camels, badgers or hares.
Moreover, it is not within our authority to change the Law if we wanted to. Deut. 4:2 states that we can neither add nor subtract to the Torah.
The story could change when the Messiah comes and as for that there is some dispute. The midrash on Lev. 11:says that the reason that the pig is called “chazir” is because in the future Hashem will return (lehachzir) the pig to Bnei Yisrael and permit it to be eaten. According to many Achronim the midrash is to be taken literally; pig will be kosher in the future. The Rama Mipano (Asarah Mamaros Chikor Hadin 4:13) explains that Hashem will make the pig chew its cud, thereby making it kosher. Critics of this point, however, argue that there is a rigid guideline that prevents this, citing the Gemara at Bechoros 5b, “hayotzei min hatamei, tamei – anything that comes from a non-kosher animal is not kosher.” Therefore if a non-kosher animal gives birth to a kosher animal (which has the kosher signs), it is forbidden to be eaten.
According to Rabbi Raphael Fuchs, Rambam (Maimonedes) would say that a genetically-engineered pig that chews its cud would also be prohibited because it is not one of the ten explicitly-permitted animals mentioned in the Torah. Hilchos Machalos Asuros 2:3. Any other animal (even if it has the kosher signs) is prohibited to be eaten because it is a lav haba michlal assei (when the Torah says you should do this it is inferred that it is prohibited to do otherwise – and the Torah says to eat these animals). It is for this reason that humans are prohibited to be eaten, since they are not one of the animals explicitly mentioned in the pasuk. However, if you hold that way it would seem to me that you also can't eat turkey because it is not mentioned in the Torah.
So, how do we explain the midrash? The Radvaz (Teshuvos 2:828) explains that the midrash is not to be taken literally; rather it should be understood that in the future Bnei Yisrael will eat mashmanim, as if eating pig was permissible. Rabbeinu Bichaiya also explains that the intention of the midrash was not to say that pig will become permitted for consumption in the future, but rather that the midrash is referring to the kingdom of Edom (which is referred to as the chazir) – that Hashem will eventually return (lehachzir) on them midas hadin (judgment). The Ritva (Kiddushin 49b) explains that the midrash is referring to Amalek.
There are opinions that suggest that a genetically-engineered pig (made with kosher signs) could be kosher if it was born of another genetically-engineered pig. This assumes the rabbinic principal that something born of a forbidden item cannot become permitted. Menachos 21a (example, boiled animal blood would technically be kosher according to the Torah, but since blood in its natural state is forbidden, rabbinically, we can not eat boiled blood, either). But once genetically-engineered pigs are born, they would become permitted to be parents of kosher little pigs. See this article from the Jewish Press.
Judaism believed that God commanded us not to eat pork, and that this will not change. (It is one of Maimonides' 13 Fundamentals of Belief that the Torah will not be exchanged for another.)
It's true that some of the classical commentaries observed that avoiding pork may have certain health benefits, but that was icing on the cake. Irrespective of the reason, when Leviticus simply says "thou shalt not", it means "thou shalt not."
Rabbinic laws (i.e. made by man) found in the Talmud sometimes were phrased as: "don't do X because of concern Y, but in situations where that concern does not apply, neither does the prohibition" -- and we may determine that in today's situations, Y almost never pops up. But we are expected to keep biblical laws no matter what reason we may suggest for them.
Note that the Bible does explain why it prohibits a king from having too many wives or horses -- "lest his heart be swayed ... lest he lead the people down to Egypt." Sure enough, King Solomon thought he was smarter than that and he had too many wives and horses -- and lo and behold, his heart was swayed and the people went to Egypt. So we don't assume we're smarter than the laws of the Bible -- even when it does give the reason for the laws, and certainly when it doesn't.
There is a Midrash (Shocher Tov 146 I think) referenced by Ri ibn Shu'aib (14th cent.) in his drashos to Torah (Matos-Masei) that pig will become permitted in the future. the Or Hachaim to Leviticus (11:7) explains that pig will change biologically acquiring the sign of a kosher animal (chewing cud in a addition to split hooves).
While some commentators understand the laws of kashrus as spiritually purifying (e.g. Abarbanel (commentary to Shmini cited and translated here), some commentators indeed presume that kashrus laws relate to health (such as those Abarbanel quotes there). They would either dismiss this Midrash (see here), posit that the biological changes would similarly make it safe to consume (assuming like Or Hachaim that its physical makeup, rather than halachic status will change), or conjecture that although it would remain unhealthy it would be permitted for whatever reason (after all, not every unhealthy food or behavior is forbidden).
Although generally the Torah's laws are immutable as codified by Rambam Hil. Yesodei Hatorah (9:1), this Midrash probably refers to the Messanic era in which even Rambam conceded changes may take place (see Hil. Megillah 2:18). Furthermore, if understood like Or Hachaim that it will change physically perhaps even Rambam would agree that with the sign of kashrus it would be kosher.
Current social changes however certainly wouldn't obviate or negate mitzvos as per the normal rules of mitzvos cited from Rambam.
It may be possible that in the light of new scientific research, perhaps involving genetic engineering, pork eating will be allowed.
In particular, a company called Modern Meadow is a working on producing synthetic meat. Tests with engineered comestible ground beef have been successful; in case pork is produced through a similar process, there is no animal per se that the meat came from.
