In my own paintings, I regularly mix different brands of acrylic paints. I've only ever had one problem and could not tell if it was the paint (it was a heavy body acrylic) or if it was the canvas...
A few words of wisdom.....I only use artist or professional quality tube paints for my paintings. You will have certain brands you prefer (as I do) and sometimes it even depends on the paint colour which brand I like.
Some brands of paint have a matte finish and some are more glossy.....this is true even within one brand of paint (Open Heavy Body comes to mind for example). If this bothers you, you can always go over top of your finished painting with the appropriate acrylic sealer (spray or liquid).
And if you are trying out acrylic-based oils, I've been doing some reading on if you can mix them successfully with regular acrylics. Seems the thoughts are mostly no, but some say they've done it without trouble. Unfortunately we won't really know until the painting ages to see if there is flaking, separation or other issues. I wouldn't chance it....use one or the other for a painting.