A lot of people who have an interest in division will claim that "this country is so divided!" but most people are just trying to get through their day and won't support a national divorce under any circumstances. Things seem more divided than they really are, especially online where most of the extremists hang out and there's no reason to compromise because it's all just theoretical / meaningless. Just people who don't know each other, and often have no way of even finding out the real-life identity of the other person, nattering at each other over whatever is viral today.
Was it Einstein who said something like, "in theory, theory and practice are the same, but in practice they are different"? How, practically, would the country divide up? You could potentially draw a contiguous country with the red states but could not do so with the blue ones. Who gets the federal stuff, like buildings, operational sites, etc. -- i.e., which of USA-red or USA-blue is the official "continuation" of the government that arose out of the Constitutional Convention in the 1780s, and which is a whole new thing? That would probably decide who gets to keep the federal stuff, it wouldn't go based on what state it happened to be in. Who gets the military and who has to build a new one? Hard border or soft border like between, say, Republic of Ireland and the UK (most pertinently, Northern Ireland)? Add in a million other practical considerations, like how to divide federal treasury funds . . . would the "continuing government" half get to keep it all, forcing the "new government" to start from scratch? Or would there be some agreement on dividing it up? Could a country allegedly "so divided" that it has to have a national divorce really come to agreement on such terms? For that matter, would the new borders even follow state lines? What about very blue parts of red states, or vice versa?
Basically, there will not be a divorce unless or until the United States, as a whole, collapses. On a long enough timescale that will inevitably occur, but the idea that it will happen because we have disagreements over abortion and transgendered people just isn't going to bring it about. I know people get angsty when the other party controls the national government, but our system contains lots of room for individual states to set their own rules - - abortion and transgender people are such areas. If you really don't like the laws you are subject to in the US, you can move to a state with laws you like better, and that's much more practical, and much more realistic, than hoping for a national divorce.