Google’s John Mueller said Google can handle sites on IPv6 & HTTP/2 all just fine with Google web search. But John also recommends that the set up also supports the older infrastructure, IPv4 & HTTP/1.x, which is typically how these are set up by default anyway, because it helps Googlebot and other crawlers & user-agents get access to your content, he said.

John wrote:

Then if you want to set to make sure GoogleBot is not having issues with your site, just use the fetch and render tool in Google Search Console and you should see right away if there are issues. John wrote:

Being in this world, it is outstanding that this person took the time to ask how going to IPv6 & HTTP/2 will impact GoogleBot. Most don’t think about crawlers and just do the switch. Of course, Google needs to make sure GoogleBot can handle it but for the most part, it should not be an issue.

Forum discussion at Google Webmaster Help.