Does it matter what the average theist believes? If Aquinas doesn't believe in the same God that a typical Baptist churchgoer does, I don't think that means that Aquinas isn't a theist.

It matters if you're arguing from a majoritarian "orthodoxy as democracy spread over time" perspective. If the vast majority of theists throughout history didn't actually believe in the God of Aquinas, but rather in the God of the old testament (or whatever), then you can't cite their belief as evidence supporting Aquinas' (or your) God.

Or am I misunderstanding your argument?