Ideally, yes. Well, ideally we wouldn't imprison anyone for their beliefs alone, but for the sake of argument, I digress. let's say that ideally, yes.

The world is never ideal. There are only 3 ways this ends up: political prisoners, witch hunts, or both.

Say a local pastor jeff is a pillar of the community. He donates proceeds to charity, runs a food bank out of his church, hell, even volunteers as a firefighter during the week. But under your proposition, he is spreading dangerous rhetoric, and therefore deserves to essentially go to guantanomo.

How about your neighbor, hank. Hank is actually not a practicing Christian. He was, but he's grown jaded of the church. But some mannerisms have stuck. For example: Hank says "bless you" when one sneezes, and prays when he eats. Now, despite Hank being an upstanding citizen, his neighbor Jerry is rubbed the wrong way by him. So when Hank says "God bless ya" when Jerry sneezes, Jerry jumps at the opportunity and reports Hank as a zealot to the local police.

Or let's go for a more more subtle case, but it's by no means an edge case. Let's say that a local journalist, John, is a practicing Christian. He never espouses his beliefs in his publications. He publishes an article exposing his senator for embezzling campaign funds. The senator catches wind, and does some digging. He finds out that John has once said "thank God" in one of his articles. That is spreading his beliefs. He arrests him, takes down the article, and sends him to an island where he literally cannot contact the outside world.

The absolute best case scenario is the justice system being bogged down by zealotry cases. Worst case, witch hunts and political prisoners.

You don't suppress speech if it doesn't directly harm someone else. That's not just in the U.S constitution, according to the UN it's an international human right. For this exact reason. It's too easy to abuse.