Is it permissible for Muslims in a non-Muslim country to recognize mosques built by the government, given their ability to build them themselves, and that the government might be seeking to appease them by doing so?

Governments establish mosques, schools, and facilities for their citizens to fulfill their interests and desires, and this is not considered a favor from them. Muslims must accept what the government has established for them and demand more of their religious and worldly rights. They should also cooperate among themselves to establish other facilities, taking care that the guardianship and supervision of mosques and schools belong to Muslims and not to others. As for the source of the funds expended by the government, it is not a condition to know it.