As far as I know all type of buildings cause cultural penalties. The overall penalty is capped on 50%, with the government type buildings having 25% and every other building 5%. I have also noticed that it is indeed possible to have buildings of other cultures while not receiving any penalty at all. If you have upgraded the government building yourself it's still possible to have a few buildings of other cultures.

As for the Mithras temples I never raze them as a barbarian faction due to both types being pagan and therefore not giving any religious troubles at all. There are no pagan barbarian temples that give such a huge happiness bonus as the level 4 Mithras temple.