Because those people feel that their culture/ideas are the correct one's and that the other county should change(Sometimes they may even be right!). They view the domestic companies as a vehicle to push their views and effect this change.

There are a couple camps:

Do business but censor, in the hopes that the users become aware and become promoters of your views

Don't do business as to not enable the regime to succeed and hope the potential users notice and become promoters of your views.

I think that for the most part, even companies like Google or Facebook will not be able to change a country, similar to how the US was not able to change Cuba or North Korea.

I think that there is a lack of understanding in Western society that other societies view their government/societal structure not as vehicles for increased personal freedom but as a structure to promote social stability over long periods of time(1000 of years. Something I think China is particularly proud of, for good reason).

I take your point - elsewhere I've said that I come from a place of pragmatism, not ideology. My question about this is that your example search engines, where this article is about Amazon selling products. I think the trade-offs are subtly different.

> The only people that care that {some company} is censored in China are distinctly people outside of China.

That's how censorship works. The people inside the bubble don't know, by design, what information has been omitted, and therefore can't care.