Slitherine

conversion bonus from piety buildings is only for religion or it will change culture too?

Manual says

10.3.2
"Remember that nobles are useful for converting
population to your own culture. So if this is a
problem it might be worth playing the appropriate
RGD to generate more nobles."

10.3.3
"In addition nobles can
convert population to your national culture. This is related to
the stewardship output in the region and the number of nobles
present."

I don't do much for more nobles so ...

Culture change will be slow. The best way to go about it is Raise your region to the ground with Pillages to sub-10 Population. New Pops will have 50% chance to become you Native ethnicity. The higher this ratio, the faster Cultural progression goes. Use Show of Authority, put Generals with Stewardship Perks on top of the region, use Governors with stewardship perks, use Ennoble RGD to create more Nobles.

The culture of the new population can either be the one of the owning nation (50% of the time) or the one of the most numerous population group in the region. The same mechanism applies to the religion of the new population. In both cases, some ruler traits are more likely to produce a population point aligned to the national faction