Great topic! I think that the answer might be more nuanced than it first appears.

First, I personally believe that a Warbird with actual service history should be painted as it was during service. Now, for many Warbirds, this still leaves quite a number of choices. For example, in SEA my airplane was originally gray, then, while still in the same squadron, painted black. Then it came back to the USA, served as a training aircraft at Shaw AFB, then with the IL ANG, and then the MI ANG. So I could chose any number of paint schemes that would be historically correct.

Second, many Warbirds had limited military service. EAA's own Aluminum Overcast is an example. It was delivered too late in the war to be deployed to combat and was quickly declared surplus and sold off. It is painted to honor another B-17 that served in the ETO. I think that this situation applies to a number of other warbirds, including some F-51's that had no combat service and are painted to honor P-51's that served in the Pacific or Europe. I suppose one could include Korea, although I have not seen any like that. I think this is a very acceptable approach, too.

Third...it is the private property of the owner, whether that be a museum, and individual, or a corporation. They can do with their property what they wish. I may not agree with their choice, but it is their choice. Even the USAF Museum works that way. One of their two F-82's is not only painted as an airplane it is not, it isn't even the correct version for the F-82 it is painted to represent.

Two more points. Gloss vs original flat. I think flat is nicer for historicity, but gloss is SO much easier to care for. My airplane is gloss black. It was flat black in service. I re-painted the upper cowling flat black both to reduce glare and to show people what the original color looked like. I probably spend more time on keeping that part of the airplane presentable than the entire rest of the airplane. Nonetheless, if I ever reach the point that it needs a new paint job...well I don't know which way I would go (maybe even back to gray.)

Interior: We need to address the interior, too. Some people try their best to keep the interior, to include all of the instruments, as original as possible. Good for them! Some people strip everything out and go for full glass on the inside. I think this misses the point of owning a flying museum. As for me, I try to keep things fairly original, to include (deactivated) armament and other equipment switches. I make an exception for avionics. My center console is modern, as I have to fly in the modern airspace system. I also have a newer AI and HSI and I am in the process of installing an engine monitor system. I make that compromise because I need to be safe and preserve the airplane in a flying status as long as I can.