Perhaps but.....
Ever see SeaQuest "Second Chances"? In it, they are back in time, they have to prevent WW III at the Cuban Missile Crisis, and Commander Ford takes a landing party ashore. They make two critical mistakes that brings unwanted attention to them. First, the Civil Rights Act doesn't exist, it is still the time of Jim Crowe, and Commander Ford is a black traveling with whites. Secondly, engineer Lonnie Henderson is a major member of the group, and they are far closer in time to a woman being June Cleaver than an engineer.
Same thing here. Assuming we buy that we had the technology to do the premise of this flick, it seems the flick is operating in the social world of today, not then. Take a look at the attitudes of then with
https://en.wikipedia.org/wiki/Ed_Dwight and
https://en.wikipedia.org/wiki/Robert_Henry_Lawrence_Jr. ("sit at the back of the capsule")
Hence, that really provides two big problems for the show. If it is not realistic to how it was then, then it has serious believability questions......and if it is, it will never fly in today's world.