Section 2, Article 1 of the Constitution states that the President is commander in chief of the Army and Navy and of the militia when called into Federal service. The National Guard is the successor of the state militias. Keep in mind National Guard units from other states have been sent to Texas to support the Lone Star State's efforts to control the border. Presidents Eisenhower and Kennedy federalized National Guard units to prevent state governors such as Orval Faubus, George Wallace, and Ross Barnett to use their military to preserve school segregation. If Biden were to do the same thing, he has precedent within living memory.
At that point, if Biden tries to take the state National Guard units away from Governor Abbott, they will either have to obey or disobey, risking courts martial in the latter case. The states supporting Texas will either have to back down or disobey. The question arises: who will blink first. In the desegregation era, it was the Southern governors who blinked.
Apples and oranges thing going on there. That was a political scuffle back then - this is an existential threat, with many layers to it. There's going to be irrevocable consequences no matter what happens.