Tolerating distasteful and bigoted opinions, maybe not. Tolerating active hate from a large group against a minority? Inevitably, every single time. (By which I mean, I can't come up with a single example - I obviously haven't exhaustively searched all of history. If you have a counter example, please share)
Yes. undeniable. In fact more often it's lead to "gay people must be fixed" which is also inexcusable, but...
"In fact, it is an inescapable consequence"
.. NO. Tolerating people having distasteful and bigoted opinions, especially when they differ from yours, does not inevitably lead to those ideas beoming reality.