Agree with mehdim - you can do both. All of my "side project" work is open source (well, %99.9 of it anyway) is totally open-source, but it's in the context of a startup where we intend to make money.
Or might they even see a startup on the side as a negative?
I'm pretty sure the answer to this is "yes" for a non-trivial number of potential employers. At the end of the day, some people are always going to be suspicious that your startup will distract you from what they're paying you to do, or that there will be some conflict of interest, or that you'll quit as soon as the startup gets some traction, and/or that you'll poach all of their good people away when it does, etc. And none of these fears are totally unreasonable. So yeah, if your startup is an ongoing concern, I would expect it would be a sticking point for some companies you might want to work for.
Does this vary by the size/type of employer?
My feeling is that larger / more bureaucratic companies will be worse in this regard, and companies that are in a field that is more closely related to what your startup does. If your startup is building mobile app games, and you go to work for EA, you might find more issues than if you went to work for John Deere or Caterpillar. That's my perception anyway. YMMV.
Does this vary by the size/type of employer?