Imo, it depends on the goals and whether they've been successful. Easiest example is mma. Studying wrestling will take away time from studying boxing or kicking. But, the goal is clear, and it doesn't really matter if someone is better at one aspect or the other.
It may be true that if one studies tcc, one's white crane may suffer -or vice versa. But, so what? If someone's goal is health or fitness, the question is whether they're getting healthier. If, otoh, the goal is fighting ability, imo not fighter cares whether they are using tcc or not. If self defense is the goal, only a fool cares about what works.
However, if the goal is maintaining a pure tradition, then of course mixing it with other things is wrong. Personally, I don't think the founders of any of these martial arts were purists. They were innovators, and It was their students who invented a tradition.
The other negative about learning multiple systems is the belief that one masters all of them, when it's hard to say if one can be mastered. And, when something happens, it's like have several cars, you can only drive one at a time. There's no time to choose, the integrated self will act. There won't be time for any confusion.
IF you ask yourself, "Should I use Yang style, Wu style, or bagua." (Answer: how did you practice to not get hit? If you did, bet they all work." If you didn't ...
"A man is rich when he has time and freewill. How he chooses to invest both will determine the return on his investment."