There is no problem with mixing Non and Synthetic fluids of any kind, whether it is Motor oil or ATX oil.
The problems come into play with SEALS and Oil.
Worn selas tend to LEAK more with Synthetic Oil than Non-Synthetic.
This is mainly because the molecules of Synthetic Oil are much smaller and uniform
than the molecules of Non-Synthetic Oil.
If your tranny has a few miles on it and you want to switch to synthetic
you should be fine and not have any problems.
If you tranny has a LOT of miles on it, switching to synthetic may be a bad idea.
Synthetic oil may run cooler, but on an older transmission may also cause internal oil pressure leaks.
I've said this in an earlier post, and I'll say it again since no one has said different.
This doesn't mean I'm right about this either, but it makes sense to me.
I have a very strong feeling that all ATX Oil is synthetic mainly because it is a hydraulic oil.
It just comes in various grades, and follows newer technological standards.
Some of the newer standards will work in low mileage transmissions, and rebuilt transmissions,
but I would stay away from them with an older transmission, at least until it is rebuilt.