R&A chief executive Martin Slumbers insists the organisation should "stay out of politics" after revealing its relationship with Turnberry owner Donald Trump has not changed since he became US President.
Golf's most influential organisations had previously distanced themselves from Trump in the wake of his views on Mexican immigrants, which were expressed when the 70-year-old announced his decision to stand for the Republican nomination in 2015.
The Grand Slam of Golf was moved from Trump National in Los Angeles, while the PGA Tour switched the WGC-Cadillac Championship from Trump National Doral to Mexico City from this year. The event was renamed the WGC-Mexico Championship and will be staged next week.
However, despite a highly contentious start to President Trump's term in office, Turnberry remains firmly on the Open rota, which will be instantly boosted to 10 courses if Muirfield votes to admit women members - at the second time of asking - next month.
Speaking after announcing that the 2020 Open would be staged at Royal St George's, Slumbers said: "I said last year we were focused on Turnberry as a golf course and there has been nothing that has happened in the last year to change that.
"I think it's very important that we're clear about what our business is, which is making sure that the Open Championship is one of the world's greatest sporting events, and staying out of politics.
"We are clearly now in uncharted territory. Sitting presidents have attended US Opens. We have not had a sitting President of the United States at an Open Championship.
"We're all learning as we go through this. But I think it's important for us that we understand where the game is and make sure we keep to that, without ignoring all the other factors that go around it."
As for Muirfield, Slumbers said the R&A would respond as swiftly to a positive vote on women members as it did when removing the East Lothian course from the Open rota after last May's ballot narrowly failed to achieve the two-thirds majority required.
"Muirfield is a wonderful golf course, it's a great Open venue," Slumbers added. "We're very pleased they are going through that process and we wait to see the outcome. We would reconsider and make an announcement very quickly if that vote comes through positively."
The venue for the 2020 Olympics in Tokyo is also under scrutiny for its membership policies, with women members at Kasumigaseki Country Club not allowed full playing privileges.
The International Golf Federation has threatened to find another course if the club does not change its rules and Slumbers added: "We are waiting to see how the clubs reacts and we will act accordingly."
Royal St George's, which voted in March 2015 to admit women members, will stage the Open for the 15th time and the first since Darren Clarke held off the challenge of Phil Mickelson and new world number one Dustin Johnson.