Wikipedia isn't exactly an irrefutable source, but it looks like those comments were made after his election.
Carlton mostly kept those views to himself when he was a player, though his teammates knew about them. (Tim McCarver once made a comment about how Carlton was always going on about the Elders of Zion and his teammates just rolled their eyes and ignored him.)
He was elected to the Hall of Fame in 1994. Later that Spring, he invited a writer from
Philadelphia Magazine out to his place in Durango, CO. And it was during that interview where his nonsense spewed forth.
http://www.thestacksreader.com/thin-mountain-air/
The Hall decided that, as he had already been elected, there was nothing they could do about it and they moved forward.
To be fair, Carlton, unlike Schilling, never looked to promote his views. (He never gave interviews and did so only because he had recently been elected to the HoF. The garbage just came out organically.) Even the author of the piece, Pat Jordan, described Carlton as being motivated by his own personal fears rather than any sense of hatred.
"He's a fearful man, one of the most fearful men I've ever met. Fear is a dominating thing with Carlton. And whenever you have a personal neurosis like that -- be it fear, anger, guilt, whatever -- you justify it by pointing to the outside world for reasons or influences. When he feels it {fear}, he hunts around, points to all these conspiracies that might or might not be related. ... He takes to heart just about anything he reads. And he doesn't see the contradictions in the things he reads."
https://www.washingtonpost.com/archive/sports/1994/04/17/carlton-talks-his-way-to-new-position-out-in-left-field/38444561-b8cf-4b49-8879-cce049207b66/
That said, Carlton is a trash human being and I've already indicated that I have no problem removing him from the HoF. Bob Ryan's take is utter, complete bullshit.