> What happens if I use Claude or ChatGPT to research sensitive social topics?

Anthropic/OpenAI is not obligated to report your use, as long as it's not violating some terribly written law (like the Florida law). The government won't know about it, so no, you will not be denied a visa.

> Many governments (especially in Latin America) copy what the US does, meaning that similar laws will be pushed sooner or later.

I honestly don't know, but I suspect most US states don't have such an overreaching law.