What philosophical evidence is there against believing in non-physical entities?

[LostLocke]

Science has not disproved the existence of other dimensions.

First off, you need to familiarize yourself more with what science does. Science doesn't disprove anything. That's not its job.
Like creationism. Technically, there's nothing in science that disproves creation, it's just that there's absolutely nothing in science that proves creation. So if you go with it you're basically saying, "There's no evidence for this idea, but I'm going to choose to believe in it anyway."
So if you're going to believe something simply because science has no evidence to disprove it, then you are quite literally going to have to believe in everything.

Why would people be unwilling to acknowledge the possibility that spiritual entities exist?

I don't know. I'm not one of those people. I freely admit it's possible that some type of spiritual creatures exist. But "being possible" is not a good reason to believe they actually exist. I need some reason or evidence that they DO exist before I start believing in them.
It's "possible" Cthulhu, Darth Vader, Sauron, Tiamat, and the Demogorgon all exist.... so I should just start automatically believing in them?