Is it permissible to compromise on prohibitions, such as shaking hands with a non-mahram woman, for the benefit of the nation, university, or students? And what are the boundaries that may not be compromised under any circumstances?

Shaking hands with a non-mahram woman is legally forbidden due to authentic hadiths concerning it, such as the hadith narrated by Ma'qil ibn Yasar from the Prophet, peace and blessings be upon him: "For one of you to be stabbed in the head with an iron needle is better for him than that he should touch a woman who is not lawful for him." It is not permissible for a Muslim to compromise on any of the teachings of the religion, because Islam is a complete and integrated whole. Allah condemned the Jews for believing in part of the Scripture and disbelieving in another part. Allah Almighty says: "So do you believe in part of the Scripture and disbelieve in part? Then what is the recompense for those who do that among you except disgrace in worldly life; and on the Day of Resurrection they will be sent back to the severest of punishment. And Allah is not unaware of what you do." It is not permissible to commit forbidden acts except out of necessity, and necessity is determined by its extent, as evidenced by the words of Allah Almighty: "But whoever is forced by necessity, neither intending wrongdoing nor transgressing, there is no sin upon him. Indeed, Allah is Forgiving and Merciful." Necessity is when a person reaches a point where, if they do not commit the forbidden act, they will perish or be close to perishing, such as someone forced to eat for fear of death. Allah has permitted uttering disbelief when compelled, as Allah Almighty says: "Whoever disbelieves in Allah after his belief—except for one who is forced [to renounce his religion] while his heart is secure in faith."