Specific sponsorship ie a company sponsoring a project and having mention/logo/link on a readme/sponsors page etc I think is quite acceptable.

A random Google ad (particularly with the privacy invasive tracking that goes with it) on the page is going to give an altogether different appearance, particularly if the project is using free resources such as GitHub/read the docs/etc.

What if Google wanted to support an Open Source project. Would it still be appropriate if the project mentioned Google as a sponsor, then showed a banner ad promoting the new Google Phone (no tracking/banner does not change)?

Saying its supported by Google and giving a link to google.com would be fine. Showing an actual advert I think is not fine.

It's not a classical open-source project, but what we did with our React.JS koans (and other our OSS repos) was to advertise our React.js book in the README and give a discount code. Essentially, it's an ad for our own book.

https://github.com/arkency/reactjs_koans

Thanks to this solution we've had more money to work on this and other OSS projects.

Looks like a great resource with a number of collaborators. What was the process of getting all the collaborators to agree to advertise the book?

Have you ever been approached to sponsor another product/company? Under what terms would you accept?

The book ad was there almost from the beginning, so we've assumed that the contributors are aware of the way this repo is funded.

As for sponsoring other products/companies - we'd need to see if it's aligned with our goals and with our target group. I don't remember anyone approaching us so far.