What surprises you about this? Historically speaking, it seems high time for a synthesis to arise.
I'm not sure what you find incompatible in "I don't believe in safe spaces" and "please stop bullying me". Hiding from bullies is a tacit concession. Confronting them is not. You might confront a bully and lose, but you might confront a bully and win, too.
Many at least - I think most if not all - who embraced the "alt-right" label, before its cynical and unjust equation by their enemies with Nazism, perceive themselves to be and have been bullied by those with whom they have the intolerable temerity to disagree. But those safe spaces which they have attempted to establish have not been permitted the conventional inviolability, but rather been gleefully invaded and their inhabitants shamed and castigated without scruple. Why "believe in safe spaces" when you are not permitted to have them, but rather encouraged with great firmness to accept that only once you have surrendered your dissent, and publicly abased yourself in hope of expiation for the sins you now forswear, will there be even a chance you may be allowed to feel safe?
As in every case where bullies run rampant and are unchecked by any impartial force majeure, the only passive defense has been invisibility, and it is very hard to remain unseen indefinitely. Your enemies only have to be good, or lucky, for a moment. You have to be good, and lucky, all the time. When you inevitably slip, or when your good fortune inevitably runs out, you are at their mercy. The social, educational, vocational, and even legal consequences can be severe - and, worse, it is not in your power whether they will be or won't be. But, like any bully, they're probably going to work you over that much harder for making them go to the effort of catching you, instead of politely submitting yourself for violation like a good little victim.
And as with any bully, there's no merit in what they do to you. No doubt every bully imagines himself enforcing some sort of right ordering upon society, in whatever sphere his power enables him to encompass. But this is a lie. The bully does what he does to his victim because his victim cannot or will not be what the bully demands he be. But even this is a lie. In truth the bully does what he does because he can, and because it's easy, and because it brings him pleasure.
Some grow out of this over time. Not all do. And power is seductive. It can easily betray you into doing things to others which you would never suffer upon yourself. It can give you any number of reasons for the former to seem virtuous even though the latter is iniquitous. The danger comes in the difficulty of differentiating this betrayal from reality. There are times when it truly is virtuous to, for example, break someone's nose, and times when it truly is iniquitous. Standing up to a bully, for example, bears virtue. Imagining one stands up to a bully, while in fact behaving as a bully oneself, does not. It is vitally important for everyone, but especially everyone with the power to crowdsource the sort of vengeful mob that can so easily destroy someone's social and professional and educational life, to bear this distinction sharply in mind. To fail in so doing risks erring into shameful, unjust, indeed frankly abusive behavior. And I suspect there are few on any side of any political divide who would be willing to argue that abusive behavior merits tolerance from those whom it would make its victims.