The simple general answer is that:
If you hold its forbidden but they hold its allowed, then you may help them to do it.
But, if you hold its allowed and they hold its forbidden, then you may not help them do it.
It all depends only on what they hold, not you.
Explanation and sources with more specifics:
The Torah in Vayikra 19:14 says "...you shall not place a stumbling block in front of the blind.." Rashi brings the Sifra which explains it to mean that one may not give bad advice to someone. The Rambam (based on Gemara) explains it to mean one may not help someone sin.
The Gemara (Pesachim 22) says that the definition of lifnei iver is that one may not give wine to a nazir or a piece of a limb torn from a live animal as meat to a ben-noach. However, the Gemara (Avodah Zara 6) explains that lifnei iver is only a problem if the wine is across the other side of the river and you are the one able to go across and bring the wine to the nazir. If the wine is on the same side and the nazir could reach it himself, then there is no issur of lifnei iver in bringing the wine to the nazir. The Rishonim discuss (linked also to a Gemara in Shabbos 3) that although there is no lifnei iver, there is a D'Rabbanan called m'sayea lidvar avera. This means that even if the wine were close to the nazir so that he could get it himself, you are still not allowed to give it to him D'Rabbanan.
The K'sav Sofer in Yoreh Deah 77 says that if the other person holds something is permitted, then you may help them, but if the other person holds it is forbidden, then you may not help them. It is obvious that helping them do what they think is forbidden is bad advice for them, causing them to sin even if you don't think it is a sin for yourself.
Reb Moshe Feinstein (O.C., I.186 by esrogim of shemittah, and Even HaEzer 4:61, by heter mechirah during shemittah in Israel) says that if the other people rely on a legitimate poseik for a heter, then you may supply them with whatever they view as heter, even if you yourself hold it is forbidden. Rav Shlomo Zalman Auerbach also agrees with this. (Minchas Shlomo A:42,44)
Shulchan Aruch Yoreh Deah 119:7, says that it is OK for a Jew who holds a certain food is forbidden to eat at the same table with Jews who hold that food is permitted (and may be eating it). The Shach explains this is because we believe that the other Jews at the table would never feed issur to that fellow Jew. So we see from here that if they would, then they are in violation of lifnei iver.
In Shulchan Aruch 163:2(also 169), we see that one may not give bread to someone who will not wash and make a blessing. The Minchas Chinuch (and Arugas HaBosem) both say that one could be in violation of lifnei iver D'Oraisa even by helping someone have bread who will not wash and make a blessing even if those mitzvos are just D'Rabbanan! After all, giving bad advice is the criteria, not the level of the sin. The Pri Megadim and MaHarshag both argue strongly against this.
It seems that the Minchas Chinuch calls it a D'Oraisa when they could not get the bread themselves. If they could get it themselves, then it would only be a
m'sayea lidvar avera. The Pri Megadim then says that a m'sayea lidvar avera (itself a D'Rabbanan) does not apply at all to a D'Rabbanan (washing, blessings before eating) whatsoever since we do not make a gezeirah l'gezeirah!
Although some other poskim argue against this Pri Megadim, the Mishnah Berurah on 163:2 does bring him at the end by saying one should "look at the opinion of the Pri Megadim". My rosh Yeshiva's son-in-law Rav Zev Smith explains this to mean that the Mishnah Berurah does not entirely endorse this opinion, but you could in fact rely on it if you need to do so.
Apparantly, this opinion holds that being machmir on a shitah D'Rabbanan about something does not mean that the machmir is making a neder (vow) D'Oraisa by being machmir (or else m'sayea lidvar avera should apply like it does with nazir).
The OP said : "..I don't mean a chumra or minhag, but a stricter position on some halacha about which there is a legitimate machloket rishonim..."
Most legitimate machlokes is usually D'Rabbanan in nature. Therefore the Pri Megadim gets you off the hook on just about any situation where your friend is machmir. But, on any legitimate machlokes D'Oraisa; or if your friend cannot get it done without you, then the heter of the Pri Megadim wouldn't help.
(On the side, Lubavitchers and other Kiruv professionals as well as businessmen dealing with non-religious fellow Jews, rely on this Pri Megadim and a Rabbi Akiva Eiger who explains that helping someone sin less is not a problem of lifnei iver. (example: eating kosher without a brachah is better than eating treif))
The OP asks: "What is the correct approach to avoiding lifnei iver in the absence of knowledge of everyone's positions on various issues?"
Certainly, to be aware of anyone's chumrah and plan for it at all times is not obligatory. This would be a doubtful "safek-lifnei iver" or less. Rav Elyashiv and other poskim permit a safek lifnei iver.
However, as we said above, the Shach on YD 119:7 says that we would never try to feed our fellow Jew something they think is forbidden. So, it is definitely proper middos to try and learn what your community and friends hold. When living among them, we should be friendly and support their potential chumras if possible, even if you are not responsible to do so.
I myself am a Lubavitcher and only eat Cholov Yisroel. Last week, I merited to sit with Rav Dovid Feinstein shelita and one of his shiurim. We were planning a siyum. The shiur had different Chassidim and Litvaks/ lower-East Siders together. One young man was joking and asked the Rosh Yeshivah if it was mutar to have a carvel turkey cake for the siyum on Thanksgiving? R' Dovid smiled and said "What about Cholov Yisroel?" The man answered: "Rebbe is the master of the place! We can rely on your father's heter." R' Dovid smiled and answered: "I'm not the master of everyone's mouth?!". (Everyone burst out laughing.)
So of course we had a siyum with only Cholov Yisroel products. I have always seen that among the greatest people, they always try to accommodate other people's needs, even when it comes to making them comfortable about their chumras.
I hope this helps. :)