What is the ruling on Muslims residing in non-Islamic countries participating in elections and voting for non-Islamic parties, with the aim of achieving benefits for Muslims in those countries?

This issue is a matter of fatwa that varies with time, place, and circumstances. Voting is not permissible if it has no effect on Muslims, or if the situation of those being voted for is similar. However, the Shari'ah interest may necessitate voting as a means of alleviating evil and minimizing harm, such as voting for a non-Muslim candidate who is less hostile to Muslims, if the Muslim vote is influential. These issues are matters of ijtihad based on the principle of benefits and harms, and one should refer to scholars who are knowledgeable of the controls of this principle and present the matter to them in detail. It is not the case that whoever advocates voting is supporting disbelief; rather, it is for the benefit of Muslims. And whoever wishes to abstain out of piety, may do so.