The numbers cited in Welch's numbers were as of 1961. Did those percentage of Catholics vs. others hold up through the decades? At least two areas of Birch Society strength, Dallas and Salt Lake City, historically have had relatively small populations of white Catholics. Additionally, the theological liberalism promoted by the Second Vatican Council had its effects on the political and social views of Catholics, as evidenced by increasingly Democratic tendencies in the suburban counties surrounding Chicago, Philadelphia, New York, and Baltimore after 1988. Many Northeastern and Great Lakes white Catholics of the G.I Generation, who listened to Charles Coughlin in their youth and admired Joseph McCarthy and Douglas MacArthur as young adults, produced Baby Boomer offspring who idealized Bobby Kennedy and George McGovern as young people and who voted in the Cuomos, the Ted Kennedys, the Kuciniches, the Bidens, and the Liebermans in the 1980s and thereafter.
OTOH, in the 1970s, white evangelical Protestants moved politically to the right, and reentered the arena of politics after a half century of exile after the failure of Prohibition and the humiliation of the Scopes trial. Before 1990, the South produced a substantial minority of white liberal politicians (though some were moderate by national standards): William Fulbright, the Gores, Lawton Chiles, Claude Pepper, Terry Sanford, Lyndon Johnson, Jimmy Carter, Ann Richards, Carl Albert, Bill Clinton. Such politicians were far rarer after 1990.
Thus, it would appear likely that the religious composition of the Birchers by, say, 1982, was more heavily weighted toward evangelical Protestants than it would have been in 1961.
If Welch were not lucid in his final weeks, one wonders how valid his conversion to Catholicism would have been. I'm not Catholic, but I would think that informed consent and an acceptance of at least the rudiments of the Catholic faith are necessary on the part of an adult before receiving baptism for that sacrament to be efficacious. Since traditionalist Catholics are separate from the mainstream of their church because of doctrinal issues, one would not think that John McManus would be involved in a bogus "conversion" of a terminally ill man.