I remember in the 2000s there was something on Mozilla’s own website that said something like “we do not support or endorse icons that say that a website is best viewed in Firefox; we believe the web is best viewed with any standards-conforming browser”. Not sure if that is still there somewhere. So that is a fairly authoritative answer as to “ethical”; in any case now that all widely-used web browser engines are FOSS, why would you want to push people to any of them?!

It would probably be possible by testing the software more extensively in Firefox.