It really depends on what you are developing. If you are using cutting edge browser features. Things like WASM or new JS APIs, sure you'll likely run into incompatibilities. However, if you are building a pretty standard content website, not a single page app, from my experience, pretty much everything just works between browsers. This was definitely not the case 10 years ago. Especially when including IE in the mix.
These days, it really comes down to “Do you need to support IE?” — even for fairly new features, if they're standard you should still check https://caniuse.com/ first but it's likely that the answer will be “Yes” for everything except IE11 and, far less frequently, Mobile Safari.
