Is HDMI 2.1 necessary when buying a new TV or Receiver?
As always: It depends. The main difference between HDMI 2.0 and 2.1 is the bandwidth the standard allows. HDMI 2.0 allows for 18Gbps while HDMI 2.1 allows 48Gbps. This increase allow plenty of new features to be implemented. Some features that are only available with HDMI 2.1 include 8K 60Hz playback, 4K 120Hz playback, Dynamic HDR, eARC, QMS, and VRR.
Those terms are all fine and dandy, but what do they mean?
Some new TVs support 8K resolution. To be able to display all those pixels, you need HDMI 2.1 to have sufficient bandwidth. This is also why you need HDMI 2.1 to view 4K 120Hz content. High refresh rate like this is mostly beneficial for gaming, as movies and TV shows are played back at a maximum of 60Hz. VRR (or variable refresh rate) also ties into gaming. When playing games, the FPS (frames per second) can vary quite a bit depending on how demanding the game or situation is. VRR syncs the refresh of the screen to each new frame provided by the source. This will make the picture appear smoother and with less tearing. If you're not planning to play games on your system, this isn't a feature you'll care about.
eARC (or enhanced audio return channel) is perhaps the feature that's most interesting. Regular ARC has been around for a while, and it allows you to send the audio from your TV, back to the receiver with 1 cable. Due to bandwidth limitations, only compressed audio was possible. This meant native Dolby Atmos could not be used, and it had to be compressed to Dolby Digital Plus or similar. With eARC you can now send lossless surround sound back to the receiver, which will do a much better job of decoding it.
QMS (or Quick Media Switching) drastically reduces the time it takes to switch between sources, and doesn't leave you with the long black screen while switching.
HDMI 2.1 is becoming more and more common, so if you're in the market for a new TV, receiver, or processor; At least you know what some of the new features involve. If you're buying new, getting a device with HDMI 2.1 might be a good idea. If you don't feel the need for any of the mentioned features, you can definitely save a few pennies by buying second hand.