What is the ruling on working for a company that cleans sofas and carpets in the homes of Christians, knowing that the homeowner's religion is only known upon entering? And what is the ruling on cleaning women's or men's salons?

It is permissible for a Muslim to hire himself out for work for a disbeliever or anyone else, as long as it does not involve humiliation or degradation for the Muslim. The proof of permissibility is that Ali, may Allah be pleased with him, hired himself out to a Jew, and a man from the Ansar did so, and the Prophet, peace and blessings be upon him, did not object to it.