Anybody should pursue the best quality training that they have available to them.
I am pointing out to the OP that if he mixes things, he may run into difficulties. His TKD teacher may take issue with some things. His teacher may say, hey why are your punches all screwy now? That may become a problem. He can decide for himself if that matters, but I am pointing out the possibility.
Now as far as consistency goes, believe it or not there are some methods that are built in a systematic way and are designed to function on a certain foundation. If you remove the foundation, or try to use the techniques without understanding the foundation, or use the techniques on a significantly different foundation, they really don't work well. Some things actually do not mix well. Chinese martial arts are usually built in this way.
So, caveate emptor. Everyone thinks they can mix whatever they want. Well sure, do what you want, it's your life. But I am pointing out that you may not get what you thought you were going to get.
Most people don't think this through the way they should, and most people mix things poorly.
But hey, everyone can do what they want. Hopefully he will be happy with his results.