A country can't convert to or adopt a different culture than the one it already has
Of course not. The cultural ideology has to be present to "convert" to it. Being present in a city different Cultural Ideologies represent people of different ethnics who share different values and beliefs.
I'd say one of the recent "conversions" happened in Bolivia. This would be equal to a change of State Cultural Ideology from Western to Amerindian. Another one would be the end of the Apartheid in South Africa: State Cultural Ideology switched from Western to African.
and being nicer to people with the same culture is less in line with the modern world situation (where trade is the main factor in international relations)
No. For example the difficulties for Turkey to become member of the EU come from the problems the old EU states have with Turkey's different culture. And this is being frankly admitted.
This is exactly how the modern version of official racism works. It is justified not by biological means as it was the fact 50-100 years ago but by cultural means ("they don't share our values..."). And it does affect international relations as shown above. We must have means to simulate this.
We already have means to simulate
- trade related effects to relations ("...appreciate the years you supplied us with resources...")
- politically related effects to relations ("...you have wisely chosen your civics...") <--- that's why I don't see the necessity of adding another political relations factor with political ideologies
What's clearly missing are means to simulate the culture effects on diplo relations. This should be weighed much less than the trade and politically related effects but there has to be a penalty when a Western or Jewish civ is negotiating with a Muslim civ. And there has to be a bonus when two Latin American civs are negotiating with each other.