Vernacular is literally what we're talking about. The definition of words.

You seem to be wrapping a number of ideas around the word Believe. Most notably the idea that a belief is fixed. When I say believe, I literally mean only and exactly "Accept as true", or "To hold as true", nothing more. It's literally the 1st definition. And more or less what all the other definitions are wrapped around.

What we hold as true can change at any time, and for a number of reasons. The study of them is called Epistemology. Yes. It's a real branch of science.

It's possible what you're trying to get across, is the idea that science accepts nothing as "true". It can only reject ideas as "false". And the ideas that remain un-rejected as false, are accepted, not as true, but as the best explanation we have so far. In which case I can see your point. However, remember that beliefs aren't fixed. They can also be rejected when new conflicting data is collected. That still sounds like what you mean by accept. Am I wrong?

It records vernacular.

And vernacular is how people understand each other. When you say, "Science has nothing to do with belief," then most people are going to interpret that according to the common-use meaning. If I say, "I believe I turned off the oven," I'm not expressing a faith-based conviction to the idea that I turned it off, I'm saying that based on my best recollection of the evidence, I did turn it off.

If you want to communicate in a way that people will understand, then I don't think you should going around using the word "belief" to mean this nonstandard, technical definition without qualifications or explanation. And I definitely don't think that you should assume that anyone who disagrees with statements made with that nonstandard definition is simply committed to rejecting reason and evidence, as opposed to the much more obvious and reasonable interpretation that they're simply interpreting the word in the standard, common use way.