I'm very concerned about loosing the right to attack religion. It's an important discussion to have and for children to see. All religion is foolish, and has to be approached from a reality-based context.
Thats a safe split: ideologies do not have (human) rights anyway...
So e.g. you can freely say that the Bible is stupid but can't say the same thing about its believers.
From the examples they give, I think you can still call them stupid. (After all, being stupid is very much part of the human condition. It's hardly a dehumanizing descriptor.) You just can't call them rats, maggots, viruses, etc. and advocate for their extermination/removal.
You aren't losing the right.
You may be losing Twitter's active cooperation if the manner in which you do so is unacceptable to Twitter, but you never had a right to Twitter's active participation in your attacks to lose.
The problem is likely greater in our corporate/mercantilist system where some state-sponsored and some natural monopolies develop. Totally get and appreciate the private property of the corporation argument...it is their town square after all...but when there is only one that is 'allowed' to succeed, what happens?
This then leads to specific tactical rules we have on the books in the US like FTC and even FCC regs, where some may protest unfair commerce.
IANAL but I can see this is a real mess. Also, what is the ROI for Twitter when it comes to policing this? We know FB has been having problems.
I think most of the things regarding regulating speech coming out of twitter are about avoiding being put in the spotlight next year in the next U.S. election. If what happened in 2016 happens again to any social network, the hammer will fall.