A man asked his wife to have anal intercourse with him. Is this acceptable behavior from the point of view of the religion?
That is an evil act. Abu Daawood, an-Nasaa.ee and others record with a good chain that the Prophet (sallallaahu alayhi wa sallam) said:
"Accursed is the one who has anal intercourse with his wife."
Shaykh Ibn 'Uthaymeen