I have delt with the same dealer (Voss Honda) for more than twenty years. Back around 2005 they allowed the entire $11,000 to go on a credit card and we earned 1% cash back at that time so $110. In 2014 they said only $500 could be put on a card, so the 2% cash back we had then was not of any value with them.That's smart. The last 2 times I bought a car I didn't finance, and they didn't let me put anything on a credit card. I may have to ask the question differently next time. I'll also have to make sure they don't charge a convenience fee to use the card.
I believe dealerships set their own criteria for accepting cards and how much can be charged to them. I was all set to put the full purchase of another vehicle in 2016 when they told me last second there would be a 2% convenience fee, negating my benefit of using the card. So yes, great point to make sure they are not charging you to use your card with them.