It's also preposterous, for at least two reasons.
First, when we do something, we are also asserting that it is the right thing to do -- if we believed that something else was the right thing to do, we would do that thing instead. (This is a slight extension of Socrates' critique of akrasia -- acting against our own better judgment -- which Socrates asserts we are unable to engage in.) In a certain sense, whenever there are two possible courses of action and I select one while someone else selects the other, I am asserting that the other person is in error. (Obviously, this applies only to actions performed with intent. When we trip and fall down by accident, we are not also asserting that others should trip and fall down.)
Now, there's a difference between describing a state ("Yams are starchy tubers") and describing an action ("I destroy yams") because actions carry the implied assertion that acting otherwise is unreasonable or immoral.
I believe it would be an error to regard statements like "I am a Christian" as descriptions of states. There is a fundamental difference between statements like "I am a Christian" or "I am a Democrat" and statements like "I am a man" or "I am a Wisconsinite." When we belong to a group defined by its ideology, we do so with intent. This is why "I am a Zoroastrian" implies that it is wrong to be other than a Zoroastrian.
Now, the position I'm objecting to here is that people are free to have their beliefs as long as they don't criticize others for not holding those same beliefs. The first part of my objection is that we are already criticizing others, simply by virtue of disagreeing with them. But one is not compelled to accept the impossibility of akrasia as a premise, as I have done, or to accept that the implicit criticism is as significant as explicit criticism (stating aloud that "If you have sex with your boyfriend, you'll go to hell," etc.) as I have also done.
So, secondly, it's important to remember that what we're talking about here are beliefs about how one ought to act. But of course, we don't act in a vacuum -- we act in response to or as a result of states of affairs ("Yams are gross, so I will destroy them"), other actions ("Yams killed my father, so I will destroy them"), and the beliefs that we hold ("Yams are evil, so I will destroy them"). And, of course, the beliefs that we hold aren't just about objects in the world, but also about actions ("It is immoral to beat your kids").
It turns out that we hold lots of beliefs about how one ought to act as a result of our beliefs ("We must bear witness to the greatness of our Lord and Savior").
This is why it is impossible to suggest that a person should A) hold their beliefs, and B) be silent about their beliefs -- because some or many of their beliefs involve the call to speech. Personally, I get on people's nerves a lot because I just keep arguing -- but I am driven by the belief that to do otherwise, to allow someone to continue to be wrong, would be immoral on my part. Similarly, the adherents of many religions are required to proselytize or outwardly express their positions.
And here's some food for thought: the belief that "You can believe what you want, just don't push it on others" is an example of a belief about how one should act as a result of one's beliefs. It happens to be a very popular one, these days (that is, it's one that we love to push on people).
Telling people who disagree with you that they can think what they want as long as they're quiet about it is, at worst, profoundly hypocritical. At best, it is a stumbling into the Cretan paradox or pseudomenon: an assertion that undermines its own validity.