Do you have a grammar nitpick that is particularly annoying to you?
Oh yeah. Boy, do I!
That and which are NOT interchangeable. I don't care how malleable and postmodern you are with the rules of the English language. They mean different things. Period.
For the official word on the difference, listen to Writers Digest.
If the sentence doesn’t need the clause that the word in question is connecting, use which. If it does, use that. (Pretty easy to remember, isn’t it?) Let me explain with a couple of examples.
Our office, which has two lunchrooms, is located in Cincinnati.
Our office that has two lunchrooms is located in Cincinnati.
These sentences are not the same. The first sentence tells us that you have just one office, and it’s located in Cincinnati. The clause which has two lunchrooms gives us additional information, but it doesn’t change the meaning of the sentence. Remove the clause and the location of our one office would still be clear: Our office is located in Cincinnati.
The second sentence suggests that we have multiple offices, but the office with two lunchrooms is located in Cincinnati. The phrase that has two lunchrooms is known as a restrictive clause because another part of the sentence (our office) depends on it. You can’t remove that clause without changing the meaning of the sentence.