Usually expanding a lot will prevent the culture victory with minimal efforts, just make sure to build a monument in every city (or play Trajan ofc) and more pop also gives more culture. Your culture income is the main defense against foreign Tourism.
Some wonders will go a long way too, they give you some tourism (not sure exactly how it's calculated, later era seems to be more tourism yield though.) so go for some wonders to boost whatever victory you are going for.
You can close borders and end your trade routes to that civ, both of those are really big modifiers to their tourism towards you.