Padraig Harrington and Rory McIlroy have both backed the decision to remove Muirfield from the British Open rota after the club voted to continue to refuse women membership.
The Honourable Company of Edinburgh Golfers (HCEG), which owns and runs the club, today voted against admitting women members with 36pc refusing their entry - a two thirds majority of those who voted was required to change the club's membership policy.
“At the end of the day the R&A have a bigger responsibility, not just to the game of golf, but to society and they’ve done the right thing” - Padraig Harrington.
That led to the venue, which last staged the Open in 2013, being swiftly removed from the list of courses that host the event.
McIlroy, two off the leader Danny Willett after his opening five-under-par at the K Club, said it was the right decision to preserve the sport's integrity.
"They can do what they want but in this day and age it's not right to host the world's biggest tournament at a place that does not allow women to become members," he said.
"Hopefully they can see some sense and we can get it back there one day.
"The R&A did the right thing. It's 2016 and we have to move with the times. It's taken long enough. Even the R&A only started letting women join last year or whatever it was [2014]. It's about time that they did.
"Bigger picture, it's a great golf course, but there's so many other great golf courses that we play on the Open rota that we're not going to miss one.
"I think it's more their loss than it is the R&A's or our loss. If that's what they want to do, obviously it's a free world and they can do that. But they must have known that it was going to cause this sort of controversy."
Harrington finished four-over after his opening round and also backed the move while labelling the Muirfield vote discriminatory.
The Dubliner told RTÉ Sport: “I suppose it was coming. We love playing the golf course, it’s a great golf course. But there’s more to modern golf than just the golf course. We see that here in Ireland ourselves.
“We’ve seen the R&A take in women members, we’ve seen Augusta take in women members. Gone are the days when you can discriminate in a club where other people want to join.
“At the end of the day the R&A have a bigger responsibility, not just to the game of golf, but to society and they’ve done the right thing.”
R&A chief executive Martin Slumbers said in a statement: "We have consistently said that it is a matter for the Honourable Company to conduct a review of its membership policy and that we would await their decision.
"The R&A has considered today's decision with respect to The Open Championship. The Open is one of the world's great sporting events and going forward we will not stage the Championship at a venue that does not admit women as members.
"Given the schedule for staging The Open, it would be some years before Muirfield would have been considered to host the Championship again. If the policy at the club should change we would reconsider Muirfield as a venue for The Open in future."
HCEG captain Henry Fairweather said: "The Honourable Company is a members club, and, as such, the members decide the rules of the club, including its membership policy.
"Women will continue to be welcome at Muirfield on the course and in the clubhouse as guests and visitors, as they have been for many years."
Scotland's First Minister Nicola Sturgeon described the decision as "simply indefensible".
She tweeted: "Scotland has women leaders in every walk of life. It is 2016. This is simply indefensible."
