The idea that marriage is inextricable from procreation isn’t a pretextual assertion or “feeling.” Virtually every human society has marriage, and until recently every single one believed that the function of marriage was procreation. Most people outside the west still do.

The four largest religions (Christianity, Islam, Hinduism, and a Buddhism) all address non-procreative sex and either discourage it or limit it to specific persons. E.g. https://academic.oup.com/book/522/chapter/135275904. It’s hard to think of anything that better qualifies as a sincerely held religious belief.