Maybe the thing which liberal/progressive types refer to as “tolerance” (in the US especially) actually has nothing to do with tolerance in the conventional sense of the word, it has much more to do with the personality trait “openness” which I guess you could also describe as “tolerance of new experience” or “tolerance of category violation”.
To me it seems ideologies and philosophy in general don’t resolve paradoxes, but they do sometimes evolve into a new thing that the paradox no longer applies to, and this same mechanism or something very similar to it might drive personality development in humans, and maybe both humans and ideologies need to change and evolve to survive. For example, “Left ideology” may evolve beyond the ‘paradox of tolerance’ by admitting that what it wants in the end is not tolerance or compassion or even justice, it wants a society as free from socially enforced borders and categories as possible, and a side-effect of this will be that people are treated equally. But equality isn’t the goal, the goal is the open society. So, intolerance of and even punishment of ‘category enforcement’ is no longer a paradox.