Is mindfulness and the acceptance it is associated with incompatible with ambition?

Not at all. When you are in a mindful state you see things more clearly. You will be more aware of what your top priorities are and it will be easier to focus on those. When you focus on your top priorities for a long time you start to achieve your goals. Your ambitions become reality without the stress associated with them.
It takes time to become more mindful, but it's worth it. Just start small. Meditate just 10 minutes everyday and write down three things you're grateful for and slowly you'll get there.
Good luck!

I believe that if your mindful enough you can still be ambitious. I find myself to be a very ambitious person with a growing amount of mindfulness. I think they agree with each other pretty well.

No, not at all. One should be mindful of their true desires in order to know where to place their intent and understand the what, where and how to apply their ambission to achieve the effect that is most optimal for themselves and the ones they love and humanity as a whole.

I would argue that mindfulness makes ambition more effective because being mindful helps you to reflect on your progress towards your goals. It also helps you rest from the high energy ambition can require.

Not in my view. Ambitious thoughts are focused on what could be. The model. Operator of Possibility.

Acceptance for what is, your current situation, is just the starting point.

Being focused on the future and being committed to the journey but detached from the outcome frees you from judgement asking the way.