I always test my forum after a theme upgrade or change with various browsers and sizes. The main browsers to test with would be Internet Explorer, Microsoft Edge, Mozilla FireFox, Google Chrome and Safari on mobile. I haven't noticed an issue with any.
I'll stop supporting Internet Explorer 11 at the end of this year. Microsoft is dropping support for Windows 7 in January, so IE should go with it. There will probably still be some stragglers, but it's a six-year-old browser and I feel comfortable with not supporting it anymore.
And now that Edge is rendered on the Chromium Blink engine, there will be much less variance in how websites are rendered. (Whether or not that's a good thing is a point of debate.) Personally, I think Microsoft's Edge engine was fine, a major upgrade from IE. It never gave me too much trouble.
But yes, a site should always be tested in available browsers and devices, especially if it's responsive. Just be glad if you don't have to test for accessibility concerns, that's the real nightmare.