You don't have to believe what you sing but you most certainly have to believe that the song is worth singing.

As an athiest I sing many religious songs because they are good songs but there are also songs which I don't sing because they could be personally offensive.

I love bawdy songs but certainly don't agree or believe in a lot that goes on in them.

They ground and ground that faithful hound

from Tenerife to Dover

Just because I enjoy singing the song doesn't mean that it's really my cup of tea.