As a European citizen, why would I want my taxes to fund a browser built by a US entity and still subject to the whims of the current US administration?

Unless you mean that Mozilla should move completely to Europe, sure. But the part about the EU not telling Mozilla what to do is naive. If my taxes pay for it, of course I want the EU to tell Mozilla what to do.

The problem is that the people in power to remove the funding are the same people who are pushing for chat control and removal of encryption. Even if say the terms says that the funding is just a sponsorship, it would encourage few government folks to look out for more knowing the company would die if they stop funding.