I count the religious right of the sixties as the very strong anti-communist electorate, and largely on the basis that Communism was Godless ( I had a liberal friend in college who scornfully lampooned the point of view as “Kill a commie for Christ”), that supported the Viet Nam war,etc., as opposed to the Episcopalians who were sending people to Cuba to cut sugar cane, etc. A bloc of voters that was led around by Jerry Falwell or Ralph Reed has never existed IMO, if that’s what you mean by “religious right.”
The fact that Communism's state church was atheism does not make anti-communists members of the religious right. True, there was a lot of agitprop used during the Cold War years warning that if the Reds took over they'd close the churches and kill priests, rabbis and pastors. But was that much different from the fear-mongering we are hearing these days that if the Muslims took over, our woumen would be wearing burquas?
I used the Episcopalians as my example to see if you'd bite, and you did. Barry Goldwater, as it happens, was one. Surprised?