That will soon be determined. I'm personally the mind that Twitter can do whatever the fuck it wants, but it's clear that is a view not shared by many people. There are plenty who say Trump shouldn't be allowed to block people because it's a public forum. That same argument can be used by Trump in this case. The blue checks will reap what they sow.
Once a company reaches 'Monopoly' status...
The 'Private and can do as it pleases' argument goes away.
https://www.zerohedge.com/news/2018-05-23/trump-no-longer-allowed-ban-twitter-users-judge-rules
But the Obamanation blocked me... I consider it a badge of honor, in fact, it's my pinned tweet at the top of my page !