Using Firefox definitely supports the existence of a free browser. Loss of market share is the #1 threat to the continued existence of a free browser. Beyond the obvious (if a tree falls in a forest, crushing the last copy of the code for a browser that has zero users, then was it a browser at all?):
lower market share =>
nobody testing against the free browser or fixing site breakage =>
quirks (bugs, underdefined specifications, nonstandard features) of other browsers becoming required for a functional Web =>
free browser is no longer a browser of the actual Web.
Being controlled by corporate interests is completely orthogonal to being free. A lot of Free Software is being controlled by corporate interests and there's nothing wrong with it.
I don’t see how just using it does. So if you aren’t contributing to it you may as well use the browser with the best feature set for your use case.