Sneakylong that the PGA Tour does not even control the major tournaments in golf (such as the Masters)
I suppose I'd need to check the qualifications for entering each of those Majors, but I believe all would hinge on a 'membership', as the base. For next year's events( Majors), it looks like the entry requirements might be set, due to 'finishing placements' from this year's events, except PGA Championship. But after that, no, the LIV players will essentially be barred from entry, unless they do get an invitation(Masters). I'm doubting those folks will invite from LIV Tour, in 2024. They would have to 'recognize' that tour's backers in the process.
The whole shitball about LIV....is political. Like we didn't know that already.