The attitude of “it works on Chrome, I don’t care about anything else” is fairly widespread anyway. Just to stem the tide a little bit I’ve been developing on Firefox and Safari first, and then checking Chrome last.
I got bitten before when I made a browser game, and then noticed that it was all sorts of broken on Edge, even though Edge supposedly had all the features I needed. It turns out that Edge did have all the features I needed, but I had accidentally used a bunch of Chrome features I didn’t need. The easy way out is to turn things off when I detect Edge. The hard way is to find all the broken parts and fix them. So nowadays, I don’t do any web development in Chrome.
But I'll admit I will also poke around outside of the tests, and I'll usually only be doing that in chrome, unless I've had a bug report about firefox in particular. And I'll only really open up Safari when I'm testing VoiceOver. ChromeVox just isn't good enough.
You can see that they should have fought harder and escalated, but issues like this are probably not the ones most upper-middle management want to potentially damage their career for.