In cases where there is a discussion among the Rishonim/Acharonim as to whether something is forbidden from the Torah (d'oraita), is it acceptable to go in accordance with those that deem it permissible (suppose they are in the majority if it makes a difference), or must one always take the stringent view, due to being stringent on cases of doubt with regards to biblically enacted commandments (safek d'oraita l'chumra)?
The OP seems to be asking about a case where one opinion says something is an issur D'Oraisa and the other opinion says it is permitted in the first place with no restriction. (There is no opinion that it is an issur D'rabbanan?)
I have seen Halachic cases like this. Although they are rare compared to D'Oraisa/D'Rabbanan arguments.
Even so, (and sometimes even if the heter is a minority opinion) sometimes, some still pasken like the lenient opinion or at least rely on them in a difficult situation.
This is because when we rely on a Rishon/Acharon as a Poseik/Rav, we are saying that the man (and his adherents, and traditions) certainly knew what he was talking about, he is correct, and we are relying on him; even if others argue. Therefore, there is no doubt involved. It is about relying.
It is true that today, Rabbis do gravitate towards paskening to the stricter view if that view holds its a D'Oraisa. This is because the Rabbi is assuming that he himself, really is not an expert to decide with his own mind when two great authorities from the past have already weighed in. He also doesn't have a reason to pick one Rishon over the other. So, he will treat it like a safek D'Oraisa L'Chumra situation and rule in accordance with the strict opinion (or at least caution that one should try to hold by it unless its a very difficult situation). Sometimes, a community has a tradition that they always held like the lenient authority in history past, and they have a right to rely on the leniency.
This should not be confused with the real use of the term "Safek D'Oraisa L'Chumra". That is applied to a situation. If a substance might have fallen into a mixture... if it was suspected to be the pork, then we are more concerned than if it may have been chicken soaked in milk.
For instance, a woman is either obligated in Birkat HaMazon D'Oraisa or D'Rabbanan. She can pick who she wishes to hold like. If she picks D'Oraisa, then if she has a doubt about having recited bentching, she may need to repeat it. If she had chosen D'Rabbanan, then she would not. (The benefit of her choosing to say she is obligated D'Oraisa, is that now she can recite it for a man and he has fulfilled his obligation.)
Picking the Halachic opinion is up to her. That is a choice, not a "safek". A situation of "safek" is then resolved based on the choice.
Hope this helps. :)
See e.g. Hilkhoth Mamrim 1:5:
שני חכמים או שני בתי דינין שנחלקו שלא בזמן הסנהדרין או עד שלא היה הדבר ברור להן, בין בזמן אחד בין בזה אחר זה, אחד מטהר ואחד מטמא אחד אוסר ואחד מתיר אם אינך יודע להיכן הדין נוטה. בשל תורה הלך אחר המחמיר בשל סופרים הלך אחר המיקל:
Two sages or two courts that argue (about a halachic ruling) either in a time without the Sanhedrin or while they (the Sanhedrin) are not sure of the thing (i.e. the correct ruling), whether (the disputed positions are presented) at the same time or one later than the other, one declares tahor (ritually clean) and one tameh (ritually unclean), (or) one allows and one prohibits, if you do not know which way the law leans, in a biblical (issue) follow the stringent view (and) in a Rabbinic issue, follow the lenient view.
In general, the rule "safek d'oraytha l'chumra" (uncertainties in Biblical law are toward stringency), is applied in cases of "safek hashakul" (halachically equiprobable uncertainties). If there is a halachically valid reason (e.g. rov - majority, chazaka - induction) to assume the lenient position is more plausible, that is the halacha. This is why Maimonides uses the language: "אינך יודע להיכן הדין נוטה" - "if you do not know which way the law leans" - "you" are the one with the equiprobable uncertainty, as opposed to the debating authorities who have legally valid opinions; and if "you" (assuming "you" are a halachically recognized authority as well) also had a reason to assume "the law leans" toward one position, then that is the law for you as well.
כיצד שורת הדין אם שנים הפוסקים כאחד זה אוסר וזה מתיר אם נודע האחד גדול בחכמה ובמנין ויצא שמו כן הולכין אחריו וכו' היו שניהם שוין ולא נודע מי גדול משניהם בשל תורה הולכין אחר המחמיר וכו'
See also the source text at the basis of the dispute (Avoda Zara 7b):
היו שנים אחד מטמא ואחד מטהר אחד אוסר ואחד מתיר אם היה אחד מהם גדול מחבירו בחכמה ובמנין הלך אחריו ואם לאו הלך אחר המחמיר ר' יהושע בן קרחה אומר בשל תורה הלך אחר המחמיר בשל סופרים הלך אחר המיקל א"ר יוסף הלכתא כרבי יהושע בן קרחה