[tmdh]

This may be unrelated. Is it legal to ship a Firefox fork as a distribution with a Chrome user agent by default?

[TheRealPomax]

as long as you don't include any of the firefox or mozilla branding, because you don't have the rights to those: absolutely.

[nerdponx]

There are also Firefox extensions that let you set a custom user agent. It might make you easier to fingerprint (unusual combination of user agent and browser features means very very high uniqueness), but it will allow you to bypass buggy user agent checks if needed.