Will I be sinful for withdrawing from a project after its owners refused to close it, despite my knowledge of the abominations within it? Is it permissible for me to donate the illicit profits from this project to a poor person with the intention of getting rid of them?

We advise you to abandon the project for the sake of Allah Almighty, for whoever gives up something for Allah, Allah will compensate him with something better. The continuation of your partners in the project will not harm you, even if you were the cause of their embarking on it, because a repentant person is not harmed by the lingering effect of his sin that he is unable to remove.

As for the profits you earned from the project: if the premises and equipment are not inherently forbidden, and likewise the rent earned from leasing them is not absolutely forbidden. Rather, if you lease these items to someone who uses them for permissible purposes, then their rent is permissible. But if you lease them to someone whom you know will use them for disobedience to Allah, then the rent is forbidden. The forbidden portion must be given in charity with the intention of purification, to clear your conscience. Sheikh al-Islam Ibn Taymiyyah holds that you are not required to dispose of such profits, for whoever repents, what has passed is his.