(CNN) Tweeting about ice cream or sending a GIF of the Pope doesn't seem particularly momentous.

But as some Twitter users are finding out, it doesn't take much to be shut out by President Donald Trump.

For Rob Szczerba, it was a joke about a new ice cream flavor.

He was making fun of Trump's baffling late night tweet where he used the now-infamous "covfefe."

"@realDonaldTrump I heard #covfefe is a new flavor from Ben & Jerry's. But it's mostly just nuts!," Szczerba tweeted at the President.

I heard #covfefe is a new flavor from Ben & Jerry's. But it's mostly just nuts! #ParisAgreement #ParisAccord — Rob Szczerba (@RJSzczerba) June 2, 2017

Soon after, he tried to send a follow up and learned Trump had blocked him from accessing @realdonaldtrump.

"When you look at all his responses to tweets ... you almost sit back and laugh," Szczerba told CNN. "It was really comical."

A Pope GIF

For Holly O'Reilly, it was a GIF of Pope Francis.

She'd tweeted one that showed the Pope giving President Trump a skeptical look with the caption, "This is pretty much how the whole world sees you."

That was her last tweet to Trump. She too was blocked from his personal account.

The pair, along with many others, are sharing their stories under the hashtag #BlockedByTrump , with many highlighting it proudly.

"It's honestly one of my proudest badges of honor," said another user, Megan Ackerman.

The last line of my resume (written in early January, obviously) #BlockedByTrump pic.twitter.com/1K768wQpFg — (((Megan Ackerman))) (@MissMeganEmily) June 7, 2017

She'd been blocked in late 2015 after she tweeted at then-candidate Trump a petition against what she said was his "dangerous rhetoric" about Muslim Americans.

"It's been incredibly frustrating as a citizen ... It feels like a disconnect from the American government and the President," Ackerman told CNN.

First Amendment concerns

When someone is blocked on Twitter, they are unable to follow the account, view the account's tweets when logged in to the service, or view tweets the account has liked.

Earlier this week, Press Secretary Sean Spicer said Trump's tweets from his personal account are considered official White House statements.

And that, some legal experts say, raises First Amendment concerns about what Trump is doing.

The Knight First Amendment Institute at Columbia University says it'll consider a lawsuit if Trump doesn't unblock Twitter users.

"Your Twitter account is a designated public forum for essentially the same reasons that open city council meetings and school board meetings are," the lawyers wrote in the letter.

For Lauren Wolfe, blocking critics pose ominous implications.

"When Trump shuts out his critics, he withdraws further into the bubble of sycophancy he already enjoys," she wrote in an opinion piece for CNN.

"Circumscribing what you read and hear becomes a dangerous affirmation that everything you're doing is right," she said.

A surprise

For Butch Parnell, being blocked wasn't so much an outrage as it was a surprise.

He'd responded to one of the President's tweets last week with, "Your days are numbered dude."

When he tried to open a different tweet from President Trump, he saw that he was blocked instead.

"In my mind, he only listens to a handful of people, and he shoots the tweets out into the universe and never even looks back at his feed," Parnell told CNN. "So it was very shocking to me that he would even take the time to hit the 'block this dude' button."