Also keep in mind Taiwan’s Tzu Chi Foundation, a charitable Buddhist organization based on the founder’s interaction with Catholic nuns. They do remarkable work, and readily acknowledge their debt to their Christian model.
And the “good works” is most likely the tie that binds them together.
But they are not Catholic.
In Việt Nam after 1975 the Buddhists and Catholics who had disdained each other for centuries discovered they had a common enemy and learned that they were compatible after all. The Buddhists did not become Catholic and vice versa except in mixed marriages (they don't stay "mixed.") Buddhist and Catholic charitable orgs cooperate with each other and will combine for actions too much for one of them. Families are tied with marriage connections now whereas before '75 Bs and Cs shunned each other. They attend each other's weddings and funerals. B and C Boy Scouts camp together. I, a Catholic taught a Buddhist the first steps to learning to meditate and steered him to a pagoda whose "abbot" I knew for more extensive instruction.