In my experience pretty much all mainstream Evangelical Christians in the United States are at least soft Dominionists, in that they believe God wants them to run the State according to their ideas about Christian morality.

I grew up in mainstream Baptist churches taking that for granted. I didn't know anyone who even thought that was a controversial idea. It was just ... obvious.

Sometimes I heard sermons about how God wants priorities in our lives, and that prioritizing obedience to God must take precedence over obeying the State. This was also taken for granted and not even slightly controversial.

The idea of pluralism, of honoring other traditions and ways of thinking, was then and remains today anathema to mainstream Evangelical Christians.

They'll make noise about "Judeo-Christian values," but they don't generally understand anything about Judaism, mistaking it for a religion that's similar to Christianity without Jesus. They have no idea how diverse and tolerant Judaism is, how radically different it is from conservative Christianity.

As you mentioned, Evangelical Christians don't believe Catholics are even Christians. You'd be hard-pressed to get them to admit that an Anglican or a United Methodist is a Christian.

So when they say "Judeo-Christian values," what they really mean are their own values. What they really mean is imposing their religious beliefs on the nation as a whole – whether or not they know what Dominionism means.