One problem with the constitution is that it doesn't actually define what a religion is. And so we are forced to take a broad definition: that religion is any belief system.
And in that vein, your idea that we should all exercise tolerance of each other's religions is itself a religion, because it is part of your belief system. It is the religion that you think the state should hold.
What I'd ultimately suggest though, is that we should have a religion, not of tolerance, but of happiness (i.e. that values people feeling good, and not feeling bad). For the most part, that would in fact mean a religion of personal freedoms, because people know best what makes them happy, and should have the freedom to do what makes them happy, as long as it doesn't inhibit other people's ability to do the same.
A religion of happiness can never be bad, because the only thing it values is the only thing that any person ever actually values as good - their own good feelings (whether they are introspective enough to recognize that or not). A religion of happiness can never lead to the violence you warn of, because violence makes people very sad, not happy.
But no group of people (e.g. a government) can ever function at all without some underlying shared understanding, which is to say, some shared belief system, which is to say, a shared religion. Whether you call it a religion or not, the government always has a de facto religion.
So the goal can never be to literally eliminate religion from the government, but simply to ensure that the government has a good religion. And the only religion that will always be good is a religion that values the happiness of its citizens above all other things. If some group of people usurp the government and institute a religion that does not value happiness in the future, then yes that would be bad. But your proposed religion of tolerance is not any more immune to being usurped than is my proposed religion of happiness. Either way, you still need the people in power to buy into it! Is that not obvious?
But a religion of tolerance is fatally flawed in that it doesn't explicitly provide a way to settle disputes. A religion of happiness settles that problem: we tolerate everyone to do whatever they want, as long as it doesn't have some inevitable conflict of interest with other people's happiness.
A religion of happiness for everyone is the only religion that will always be good for everyone, whether everyone recognizes it or not. And so the goal of any thoughtful and introspective person should always be to push for a government that values the continued happiness of its citizens over all other things.
