How do I consult my heart when there are two strong opinions on a religious matter, is there a specific supplication for that, and is it permissible to pray Salatul-Istikhara to choose between them?

It is not a matter of consensus among scholars that a questioner may choose one of several equally valid opinions. Some have gone so far as to say that it is obligatory to adopt the stricter and more cautious view because giving a choice abrogates religious obligations and leads to following desires and whims, and because the Sharia is based on a single ruling.

Therefore, the questioner should employ some form of preference, such as preferring an opinion due to the greater knowledge or piety of its proponent, or by adopting the more cautious view. There is no objection to preferring an opinion through Istikhara (seeking guidance from Allah) as it is the closest to what is correct.