Nonsense, we most certainly can. In fact, most countries "worked out" without ever needing to be tolerant in the first place.
Popper doesn't even acknowledge that this notion can be universalized, and then you're just back to square one with Carl Schmitt and the Concept of the Political.
Take your LGBT example. For that to work, you must be intolerant of, say, Salafis. Then the Salafi can respond that his in-group (the faithful, true to God, whatever) are being threatened by those who must necessarily be intolerant of him by nature of their own allegiance.
Thus you still end up with a value judgment despite Popper's veneer of neutralization and depoliticization. That's where the real philosophizing begins. How do you justify allegiance to one side of the friend/enemy distinction over the other?