The PGA Tour took the decision to suspend members who have competed in the Saudi-backed breakaway without prior permission.
The DP World Tour, on the other hand, fined played £100,000 and banned from the Scottish open last week, but saw that temporarily stayed on appeal.
Last month, the R&A announced that LIV players who were exempt from the Open would be given permission to compete at St Andrews. This follows the position taken by the USGA ahead of the US Open.
Despite this, USGA chief Mike Whan warned that in LIV players would face a harder path to qualification in the future.
That view was echoed by R&A boss Martin Slumbers who said: "Looking ahead to the Open next year, we have been asked quite frequently about banning players. Let me be very clear, that's not on our agenda," Slumbers said.
"But what is on our agenda is that we will review our exemptions and qualification criteria for the Open. Whilst we do that every year, we absolutely reserve the right to make changes as our Open Championships committee deems appropriate.
"Players have to earn their place in the Open and that is fundamental to its ethos and unique appeal.
"I never said the best golfers would not be able to play. We will hold totally true to being open to anybody, but we will look at whether it is an exemption or through qualification."
The biggest exemption category for the Open is for the top 50 ranked players in mid-May. This, in turn, makes LIV Golf's application for the right to offer ranking points vital.
"Professional golfers are entitled to choose where they want to play and accept the prize money that is offered to them," Slumbers added.
"I have absolutely no issue with that at all. But there is no such thing as a free lunch.
"I believe the model we have seen is not in the best interest of the sport as a whole and is entirely driven by money, which we believe undermines the merit-based culture and the pursuit of open competition which makes golf so special.
"In my opinion the continued commentary that this is about growing the game is just not credible and, if anything, is damaging the perception of our sport which we are working so hard to improve.
"We believe the game needs to focus on increasing participation, achieving greater diversity and making sure golf is truly open to all rather than this narrow debate involving a small number of players."