Why does Minecraft show this crash report about 'BlockEntity' when I try to log into certain servers?

I had this exact issue today with 1.10.1

Try setting your version back to 1.10, I have had no issues with that.

If you don't know how to change your minecraft version, look here: http://gamingedus.blog.ryerson.ca/educator-minecraft-resources/minecraft-how-tos/changing-your-minecraft-game-version/

Setting the version back, anything besides 1.10.1 that the server still supports, seems to work for me. I had the same issue with Wynncraft

Based on this thread in the Minecraft Forums, several people are seeing this with v 1.10.1.

One of the Minecraft devs is asking people to report this error, and even mentions that they plan to release 1.10.2 later today with a fix:

I've been told that we'll have 1.10.2 later today as well, because there is a crash happening in 1.10.1 that we didn't get in testing.

In the interim, flip back to an earlier version and you should be ok.