I don't think that the vast majority of atheists are being deliberately insulting when they say that somebody who holds a religious point of view is delusional. The crux of the atheist critique is, after all, that religion is a form of superstition. If religious people find that offensive and insulting, it is what the atheist honestly thinks, and, so long as atheists aren't personalizing things it's something religious people have to put up with in a democratic society. For the most part religious people do just that. knowing that they are quite capable of dishing it out as well if they need to - I had a Muslim friend years ago who used to mock my defence of Darwin by calling me a monkey. You can put up with things like that if you know there's no bad intent involved.

"saying you believe in something that isn't based on fact or evidence makes you exactly the same as those who do."
That seems to be saying that a truthful religious person is exactly the same as an atheist who is deliberately telling lies, and that, what atheists have in the past regarded as religious delusion ,is in fact a lie perpetrated by billions of people every day, world wide.Perhaps that is what religious people find offensive - atheists effectively calling them liars ?