No, Firefox allows you to rebrand modifications and so is Free Software. If it enforced that you keep the branding, that would be non-free.

Here it is right in the list of APPROVED Free Software licenses: https://www.gnu.org/licenses/license-list.html#MPL-2.0

You're talking semantics. Sure, the branding is non-free (you can't distribute the same version obviously), but your four freedoms aren't diminished in any way [1].

[1]: http://www.gnu.org/philosophy/free-sw.html

Firefox is non-free due to trademark protection, but that's VASTLY different to being non-free due to being a paid download, or being closed source, or patent licensing, or restrictive licensing terms, and so on. It's almost irrelevant to the parent poster's comment to claim that.

Firefox is NOT non-free, period.

https://www.gnu.org/licenses/license-list.html#MPL-2.0

No, there are disputes over this, and it's exactly why there is Iceweasel in Debian:

http://en.wikipedia.org/wiki/Mozilla_Corporation_software_re...

It's not really a big deal, but the trademark restriction does mean you can't just redistribute Firefox as-is. Whether you count that as non-free is subjective.

I agree there's some subjectivity but "you can't just redistribute Firefox as-is" is NOT subjective. That is flat out wrong. You can redistribute Firefox as-is. What you can't do is redistribute modified Firefox and keep the name.