Is it permissible to sell a house to a non-Muslim who deposits his money in banks, and is the prohibition due to his being a non-Muslim, or because of his involvement in usury, or both?

There is no harm in selling a house to a non-Muslim, for the Prophet, peace and blessings be upon him, and his Companions dealt with disbelievers in buying, selling, and leasing. There is also no harm in selling a house to a person who receives usurious interest on his money deposited in the bank; because dealing with a person whose money is mixed [with usury] is disliked (makrooh) but not forbidden (haram).