I love flying 172s as much as the next guy, but I gotta admit my heart is in warbirds.
I've heard of a few that do the whole volunteer flying warbirds on their time off from the airlines. But would there be any way of doing that full time? Ideally that would be my ultimate long-term goal.
I know that as a 1000ish hour, early 20s CFI with no ATP, my chances are pretty slim at the moment. But I don't mind waiting. The question is, how can I start investing my time so one day I can reach my goal?
There are a few ways to get into warbirds. It helps to have some money.
The easiest and arguably best is to buy your own and then you don't have to deal with the politics, but most folks don't have those kind of resources.
So, you either need to know someone and be invited into the inner circle, or join the CAF. The CAF is probably the easiest and a potentially good network tool, but beware: like a lot of big organizations, there are some truly great units that are committed to sharing history with the public and there are some units that seem hell bent on perpetuating the CAF's negative reputation from a couple decades ago. Hopefully you are near a good unit.
Outside of the CAF, I'd suggest finding someone near you who does warbird flight instruction (something like a T-6) and get a couple hours of dual and start a relationship/network. In time, they may be able to open a door or two for you.
If you are serious about warbirds and want to someday fly the more exotic stuff (P-51, Wildcat, Corsair, Avenger...etc) then you will need lots and lots of T-6 time (100 hrs seems to be the magic number). Find someone to partner with and buy a T-6 (you can get an airworthy one for time building in the $100-125k range), fly it to shows, network and as long as you aren't a jackass, the flying museums will open their doors to you in time.
That said, I don't know too many people who fly warbirds full time. Most have side jobs and fly when there is a show or rides to be flown. The handful that do it full time are guys that have a ton of experience and offer flight instruction in the warbird(s). And I suspect that even those guys have other business ventures/investments that provide additional income.