As you might guess I'll take science over junk science and personal anecdotes.

600K Americans died of the flu pandemic in 1918.

Flu and flu vaxxes would not see breakthrough infections and deaths of over 800K and counting.

So there goes your 'just a flu' theory.

But let's say that you test positive for Covid. You really going to go to the Y, and possibly infect others, to test your sauna theory?

Bet they want proof of vax, for just the risk I've described.