The Majors are there own entity, they set their own rules and will set their field as they see fit. I don't anticipate any of the LIVers being banned from any of them. They could be persuaded by the PGA and Euro Tour to take some action, but I doubt it.
Any Major winner gets a 5 Year exemption to the other 3, so both DJ (2020 Masters) & Phil (2021 PGA) will be eligible for the next few years. For Phil that really only matters for the US Open. He's won the other 3 so as former Champion he's eligible for the Open until age 60 and the PGA and Masters for life. DJ won the US Open in 2016 which gets him a 10 year exemption through 2026 for that event.
Any non-Major winner could have difficulty though. For example the Majors usually save spots for the Top 30 of the PGA Tour from the previous year. If the players are no longer in good standing, they could cancel their invitation.
If they are not Major winners, starting next year, I suspect they will have to rely on the spots reserved based on World Ranking or for the US Open and Open, have to go the local/regional qualifying route.
Another impact to be seen is Ryder Cup eligibility. The Ryder Cup is not affiliated with the PGA Tour, but it uses results from those events to determine the squads. Could still be eligible as Captains picks though.