What is the correct Sharia stance on adopting the principle of public interest in the West, supporting those who advocate for the rights of homosexuals, shaking hands with women, not growing a beard, and taking out interest-based loans to buy a house, in order to avoid Muslims being labeled as backward or racist?

Islamic Sharia (definition) is based on achieving benefits and minimizing harms. The balance between them is precise and can only be managed by skilled scholars. Ibn Taymiyyah clarified that conflict is either between two good things, in which case the better of the two is preferred; or between two bad things, in which case the worse of the two is averted; or between a good thing and a bad thing, in which case the more preferable is chosen.

For example, perversion is a great major sin, and it is not permissible to compromise on it under the pretext of reducing racism. Similarly, usury is a major sin and is only permissible in extreme necessity; the need for housing can be met by renting. As for shaking hands with a non-mahram (definition) woman, it is forbidden, and the harm of a woman's aversion can be averted by explanation and clarification. Shaving the beard is forbidden, but it is permissible under duress or necessity that prevents a person from working and supporting his family, from the perspective of committing the lesser of two evils.