That hasn't been the case for a pretty long time. Now the permissions are quite granular and you can accept and refuse specific one at any time. It's actually quite tiresome to go through 4-5 permissions popup on some apps, but it makes sense so it's okay.
The apps is informed of that decision, so yeah it can decide to not works without it. I suggest you to not use an app that require stuff that you don't want to allow.
> That hasn't been the case for a pretty long time. Now the permissions are quite granular and you can accept and refuse specific one at any time.
This is technically a correct answer, but I've seen the bad habit of asking for many permissions (and sometimes refusing to work without) being more common on Android. An example is a bank's app that will refuse to launch (or I mean, provide any meaningful information/experience) unless location permission is given (this is when giving the permission means an "always allow") and unless it's connected to a cellular data network (not WiFi). On iOS, the app is better behaved and will work with some useful functionality when certain permissions are denied.