If your browser's development console reports your connections to our server using HTTP/1.1 and you have ssl enforced within Plesk, the answer lies here: https://www.nginx.com/blog/supporting-http2-google-chrome-users/
The gist is that browsers have dropped support for HTTP/2 NPN in favour of the ALPN protocol, even though ALPN is not available on many servers that are the backbone of the Internet. We believe they should have waited until CentOS6 / RedHat Enterprise 6 reaches end-of-life in 2019 as this operating system is used on a massive number of web servers. Unfortunately they did not.
If you're having this problem, then your server must be running CentOS 6, which does not support the ALPN protocol, which is required in Chrome to use HTTP/2. Safari uses both NPN and ALPN for HTTP/2 connectivity, and thusly supports HTTP/2 on this server.
Unfortunately we can't upgrade the server between major versions without encountering serious problems and we also can't manually recompile both openssl and *all* server dependencies every time there's a security patch across all of our servers: it's simply not feasible.
What this means is that we're stuck with some servers not being able to support HTTP/2 with ALPN (though HTTP/2 with NPN is working) until they're retired in a couple year's time: CentOS 6 goes EOL in about 2 years. It's likely we'll be migrating clients to newer systems within that two year window.
If your site requires HTTP/2, we recommend a dedicated VPS running CentOS 7.
