I am pretty sure that they ask if you have had ANY vaccines in the last 90 days(30 days???) not just rabies when you donate blood. At least with the American Red Cross.
"They" do things differently, depending on which organization you are donating through.
Our of curiosity, I went and reviewed the questions the group I donate through asks. It's the "other" big blood organization in our area (I don't know how widespread they are, but up here it's basically them and the ARC, I think.).
They don't ask about any normal vaccines. They don't ask about rabies, either pre- or post-exposure.
They do ask about "experimental" vaccines. And they have a laundry list of drugs you can't be on or have used recently. Places you can't have traveled within a certain time frame. The whole gay or sex-for-money stuff. Your own health status. Tattoos/piercings.
Most of the drugs they ask about are because either the drug/vaccine doesn't actually protect you from infection (and therefore you could still pass it on to a recipient), or because of some other possible detrimental effect (like for a pregnant recipient, for example).
You're right that ARC asks about vaccines. But they distinguish between inactivated and modified live viruses with regard to deferrals from donating.
Bottom line: It appears to differ somewhat organization to organization, and state by state.