Blocking screenshots or screensharing has nothing to do with hardware acceleration / graphics acceleration.
It is, in fact, deliberate blocking of any capture of the video through DRM, by not letting any other apps besides the browser and the operating system access the video content.
If you leave hardware acceleration on, you'll note that you can take screenshots of any YouTube or Tumblr video out here. This disproves the last post's assertion.
That being said, yes, disabling it does work for taking screenshots of HBO Max or Netflix, and the reason why is because DRM like Widevine — which is what's used by browsers, iOS, and Android — generally requires hardware acceleration to be on, because their highest levels require trusted execution environment hardware.
If you disable hardware acceleration, DRM might be disabled altogether — but usually, it will fall back to a lower, software-based level (like Widevine L3), which is more permissive.
You can read more about it here and here.
On Netflix and most other DRM-protected services, being on Widevine L3 means that you are stuck with 480p or 720p maximum, even if your plan should let you access more.
Disabling hardware acceleration is also a terrible idea in general. To put it succinctly, your CPU will be forced to work much harder when browsing web pages, and especially when it has to decode video. Don't be surprised if you see your battery life decrease, or if you feel your laptop heat up more.
You should always leave hardware acceleration on in your various apps, because letting them use your GPU instead of your CPU for various rendering tasks is much, much more efficient.
So don't forget to turn hardware acceleration back on when you're done!