Most acrylic paints have to be on the alkaline side of the pH range for stability. However, some manufacturers tend to leave paints on the low side and others on the high side. When these opposites meet, a pH shock occurs and the mixture can be lumpy like cottage cheese. It tends to be temporary and normally will smooth out if they are mixed for a while.
If the paint mixture begins to get very lumpy, mealy, stringy, or some other adjective that should not belong next to the word paint, there most likely really is an incompatibility and I would suggest not using that mixture.
-- Michael S. Townsend, Technical Support team, Golden Artist Colors, Inc.
In my own painting I regularly mix different brands. While I do have favorite brands, I do like to try new colors and unfamiliar brands (see How to Assess a New Paint). I've not encountered problems with paint interacting -- no cottage-cheese textures or adhesion problems -- but I have inadvertently used a slow-drying acrylic when I wanted something to dry rapidly (see Drying Times for Different Brands of Acrylic Paint). Annoying, but not disastrous.