Perhaps Close, and her father, were with a part of MRA that practiced them in the extreme. Or perhaps her father was a domineering, patriarchal type, and MRA provided a rationale and framework for him to justify personal authoritarianism.
Moral Rearmament came out in the interwar period, and was based on the belief that radical Christian living could transform individuals into more loving people, and if this spread, could lead to world peace. They deliberately targeted leaders in business, academia, and government. For a while they were active in (early) Nazi Germany, but were eventually closed down. Because of their outreach to leaders, they were regarded by many as spiritual elitists. Known first as "the Oxford Groups," it was considered a spiritual movement, and not a religion, and its "Six Steps" were the foundation for AA's Twelve.
Close noted, in the brief article, that she called her father, "brilliant, brilliant..." and MRA as "cult-like religious group," -- not quite a cult. My guess is the issue is the father-daughter relationship, not the spiritual one.
I think trying to draw some kind of line between what is or isn't a cult is like trying to draw an exact line between mentally ill and mentally healthy. "Not quite a cult" might not be full blown cultism, but it's not harmless, either. Cult-like things should be avoided no matter how slight.
There are a number of lists out there, plus plenty of articles. They've been posted here lots. I just don't think the Oxford Groups/Moral Rearmament qualified. Glen Close is the first I've ever heard of anybody making such a claim--not that I've studied this. Just a bit of background reading in my early days of 12-Step Recovery.
On the basis of minimal information, I think this is a Glen Close/controlling father issue. Contributing to my conclusion is a bit of generalizing: anti-relgious sentiments are common in Hollywood, as are various types of victim mentalities. Those factors might be involved.
She's listed on this TV soundtrack album as "Gleen Close"--mid 1966. UP WITH PEOPLE is the record/music/touring arm of Moral ReArmament. The Brigham Young University Singers - Sounds of Freedom - BYU Young Ambassadors - Grand Land Singers were at least partially based on UWP, using many of UWP's song catalog in the '60s and early '70s.