If "Reuven" believes the halacha to be one way and "Shimon" believes it to be more lenient may Reuven rely on Shimon to do something for him based on this leniency?
Here is a 100% fictional practical example to illustrate the concept that I am asking about, please note I am NOT posing this as the actual question, the actual question is what was stated above: Reuven's Rav has given a psak that not using a kli sheini is bishul m'deoraita. Shimon's Rav holds you can use a kli rishon. Can Reuven drink a tea made for him by Shimon?
Even someone who does not open cans on Shabbos may use a can that was opened on Shabbos even if they were opened for him (Iggres Moshe: O"C Chelek Daled Siman Kuf Yud Tes Ois Heh) and does not require the person who opened it to drink from it. Non the less he may not ask someone to open it for him(Kuntres Yad Dodi, Harav Dovid Feinstein,pg. 31).
This is not necessarily an answer that applies all across the board, but at least it does indicate that such a principle exists.
In summary, according to the Sha’ar Ha-Melekh, you may not assist someone to do something you consider forbidden even if he follows a different legitimate view. According to the Mabit, Kesav Sofer and R. Auerbach, you need not be concerned about lifnei iveir if someone follows a legitimate lenient view.
From what we have discussed, it seems that during the week you are allowed to ask someone to do something that your rabbi considers forbidden but his rabbi considers permissible. R. Shlomo Zalman Auerbach and others rule that lifnei iveir does not apply and most authorities follow Rav Sama, that ein shali’ach li-dvar aveirah still applies. Halakhic pluralism means accepting that someone else may legitimately follow different religious practices than you.