Both of your examples are kind of monopolies

Is there any car software that’s “open”?

openpilot is an open source advanced driver assistance system that works on 250+ car models of Toyota, Hyundai, Honda, and many other brands

https://www.comma.ai/openpilot

Can I run their software on Tesla?

There are examples of this, yes [0]. The phrase "run . . . on Tesla" might have different meanings. OpenPilot is not installed directly on the Tesla hardware (as far as I'm aware). OpenPilot runs on separate hardware that communicates over the car's network, typically CAN bus [1]. An analogy might be attaching USB devices to a laptop, which has its own video, sound, keyboard, and pointer; but for which a user might desire some other feedback and control method.

0. https://teslamotorsclub.com/tmc/threads/say-hello-to-an-fsd-...

1. https://en.wikipedia.org/wiki/CAN_bus