If Tyrion is a Targaryen then I don't like it. Oh look, another character is secretly a Targaryen!!! What a twist!!! It removes all the impact of Jon's own reveal. It also vindicates Tywin's behaviour towards him which devalues that story arc altogether.

I also think people who subscribe to the theory are wilfully blind to the repeated theme that Tyrion is Tywin 2.0.