I feel as though McIlroy's public comments have been in this vein for several months now. He obviously doesn't care for Norman, but the fact of the matter is that if LIV were truly seeking to work with the PGA Tour in a collaborative manner that would allow the two to coexist and complement one another, Greg Norman would be possibly the worst choice to head up LIV.
To LIV's credit, they've purposely avoided scheduling events that conflict with the majors, for obvious reasons, and the PGA Tour's elevated events. Which begs the question, why wouldn't the PGA Tour welcome the LIV contracted golfers to these events if it it elevates the quality of the field and viewership interest? Most of the guys on LIV didn't support lesser PGA Tour events when they were PGA Tour members anyway, so it's really no loss to the Tour as far as the quality of field that shows up to a Sanderson Farms Championship, Valero Open or John Deere Classic, to site some examples. Those events should either a) disappear entirely from the Tour calendar or b) become Korn Ferry tournaments.
The problem is you have butt-hurt, egotistical jerks running both leagues. The best thing that can happen is for both Jay Monahan and Greg Norman to step down from their respective positions and hire executives willing to make this work for the benefit of all. There will most likely be a merger of the two at some point, but that's year's off in the distance.
In short, this doesn't have to be an "us" vs. "them" proposition. Were Rory McIroy, Jordan Spieth, Justin Thomas and Jon Rahm to walk into Jay Monahan's office today and present him with an ultimatum to the effect of "Allow the LIV guys to play whatever PGA Tour events they want for the good of the league or we're walking", watch how quickly Monahan capitulates, as their defection would seal the demise of the PGA Tour as an ongoing concern. The upside to this is that it would allow all top professional golfers to play in LIV events and sign team contracts. Seeing the league only plans to have 60 rostered golfers going forward (one alternate on each team), this leaves a good chunk of non-LIV talent to play the other tours and flourish there.