If I start a school that teaches kids how to make bombs and tell them to Destroy the Capitalists, am I on the other side of that line?

Yes. This is not a religious activity, but an incidence in which religion has stepped over the line into political action. Not to mention conspiracy to commit vandalism, arson, and murder.

Churches, and other religious congregations, are not permitted to preach for or against political parties or candidates because this is considered a breach of the church/state barrier from their direction. They also are not allowed to advocate that individuals belonging to their congregations commit criminal acts because this, too, strays into the state's realm. Religion retains its right to speak out on moral issues, but is not permitted to teach or advocate action that destabilizes the political structure of the community.

If I teach that Jews are evil, does that cross the line?

Alas, no. Bigotry is not a crime. If it were, I know of Protestant clergy from my childhood who would have had their asses in a sling because of the things they said about Catholics.

It's perfectly legal. "...and we must therefore destroy them", now that's illegal. It steps into civil jurisdiction.

Whether bigotry is moral is another question. But that question is one for religion to answer, not the state. The state cannot enforce morality. The state has its hands full just enforcing the law.

And even if no legal action is possible, one can at least expose them.

Yes, but not through the use of government agencies, agents and equipment without a full-blown criminal investigation, complete with all the warrants. Civil authority cannot traipse all over the First Amendment rights of any religious group. Well, it's not supposed to. The Branch Davidian incident shows that it can and does happen.

If there is sufficient, legally obtained evidence that leads to suspicion of illegal treading into the civil realm, government may investigate a religious group. But government may not place private religious organizations under heavy surveillance because some co-religionists have committed or conspired to commit crimes. If the local police want to put an extra patrol on the public street on which a congregation's building is located, well, that depends on the department's budget, doesn't it?

Investigation of stuff like this is the press's job. That's part of why we have them around.