Firestone historically had a very close relationship with Ford, which is why some of you are seeing original cars with Goodyear tires on them. I actually believe that I have some original documentation for my 70 SS that states Firestone brand but I'd have to look to be certain.
The only reproduction tire available for our cars is a G70x15 Firestone Wide Oval tire. This size has the proper 3/8" white wall. You can't get the G78-15 that would be the original standard size for small block cars either.
If you are looking to go to AACA judging (I'm a senior master judge in their organization and the Assistant Chief Judge for Hershey this year and Chief Judge for 2016 and 2017), the brand does not matter. The tires only need to be the proper size and construction.
If you are lucky enough to find an original Goodyear, it may hold air but the properties of the rubber are probably degraded to the point where they would be unsafe to drive on. The reproduction bias ply tires are quite safe to drive with, provided that your alignment shop sets the front suspension to the factory specs. The specs for radial and bias ply tires are different, hence the Pontiac trademark of "Radial Tuned Suspension". I can attest to this difference on my 66 Ford Galaxie. It's a 60K mile original and when I brought it home it drove like crap with radial tires. It wanted to wander all over the road. Since we were showing in AACA I immediately put a set of bias ply tires on it. Now it drives straight as an arrow. Between Dad and I, we have 4 cars running bias plies and haven't had an issue with any of them.