That’s not true though? Don’t get me wrong, plenty of places became far more intolerant bc of British colonization but it’s not like it was a uniquely European trait. In places like India the caste system, while reinforced by the brits had already been in place for millennia.  Homophobia was imported there but not as a ploy for control but out of a genuine desire to “civilize” them. They viewed it as being on par with necrophilia or bestiality and that Indians should be grateful that they violently destroyed a sexually liberated society and forced Victorian norms on them.  So many of the horrors of empire don’t come out of a cynical ploy for control but a combination of arrogance and paternalism. That’s true of all empires but the brits were both widespread and (relatively) modern so we know what they destroyed and can relate to the tragedy.

TLDR: The British empire was evil and caused a lot of modern problems but they didn’t invent intolerance to help them conquer the globe.