So, there's no way to do this with plain standard options and "expect them to interact with collisions or dynamics". I can add smth like Frizz animation for particular time segments to avoid intersection with the other hair selection set, right?. Much better! But this won't give me any collisions.
Maybe, there's another way and you can guide me to the right direction? What if ..to try something like duplicate and hide collider object (let's call it Head) and split set selections between the heads. Therefore, I'll have 2 heads with different hairs (selection sets). And then these hairs of different objects may interract with dynamics...? I tried to make a test, but stucked because I still have to deal with a hair collider (of copied head) for the "second" hair and somehow make the other "first" hair (of main head) be a collider for the "second"