Let's ignore the cesspit that's Twitter for the moment, since I don't know how it works, and focus on interactions in the real world.
> They hate the idea of getting in trouble for using the wrong pronouns for people
Relatively rarely happens. Does tend to happen if you repeat it consistently and show no attempt at learning - at that point, it's subtle bullying and disrespect.
> having to use non-traditional pronouns at all
Most enby people I know are at least not actively uncomfortable with people using binary pronouns, although I'll continue to point out that singular they has been correct grammar for longer than anyone has been alive. They might decide to pursue activism towards greater awareness, and some of that is likely to be student activism - they're also likely to create and participate in social spaces where they're respected. It's generally not a problem in workplaces, since enby people are almost universally terrified of being out about their gender at work.
> They were very upset about stories of people being suspended from elementary school after using the wrong pronoun
Doesn't appear to have actually happened. Some kid got sent to the Principal's office once, and I assume got talked to and sent back to class, since no news source says anything else. I can't figure out the actual details on what happened to cause the kid to be sent to the office, since every news story on the subject seems to have a different set of facts, strongly suggesting that at least some of those facts were partially made up. I suspect some teacher was on edge about potential bullying - which definitely happens - didn't realise the kid didn't already know, and the issue probably got resolved without any lasting harm to anyone.
> They were upset about a professor getting in trouble for wanting to only use male and female pronouns based on biological gender
Now that we're talking about adults in an educational setting where people are intended to interact professionally with each other, a failure to respect the adults you interact with - and the people who part-fund your job, at that - is likely to get you fired, yes. The only way you can twist this to be a bad thing is if you thoroughly believe that people with nonbinary genders are not worth respecting.
> They feel like they cannot express their views without being attacked
How do they think many of us feel, and have felt for decades? We spend ridiculous amounts of energy trying to calm their fears, anyway - I spend much of my social time explaining to people in real life why their (usually unintentionally) misguided ideas about trans people are based on incorrect facts.
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I don't know how to solve these problems. Most of it is continued education, but how are we going to educate people when there's systems in place - often religious and political - specifically intending to keep people in the dark about reality?