Former Ohio GOP Gov. John Kasich learned the hard way Monday that just because he's anti-Trump, that doesn't buy him full acceptance into the Democratic Party.

Kasich was reminded of his second-class membership on the left by Rep. Alexandria Ocasio-Cortez (D-N.Y.) after Kasich commented in an interview that Ocasio-Cortez didn't represent the entire Democratic Party base, which Kasich believes is more moderate.

"I think both parties have to have new ideas, and I think this country is moderate," Kasich said. "People on the extreme, whether they're on the left or on the right, they get outsized publicity that tends to define their party. You know, I listen to people all the time make these statements, and because AOC gets outsized publicity doesn't mean she represents the Democratic Party. She's just a part, just some member of it. And it's on both sides, whether it's the Republicans or whether it's the Democrats."

Ocasio-Cortez didn't appreciate being name-dropped by Kasich, nor did she think the former Republican presidential candidate had any business speaking on Democratic Party values.

"It's great that Kasich has woken up & realized the importance of supporting a Biden-Harris ticket," Ocasio-Cortez responded on Twitter. "I hope he gets through to GOP voters. Yet also, something tells me a Republican who fights against women's rights doesn't get to say who is or isn't representative of the Dem party."

"We can build bridges & not lose sight of our values," she continued. "It's important to remember that Kasich is an anti-choice extremist. He 100% will (and has) signed away our reproductive rights the moment he has the opportunity to do so. He is not a friend to workers."

To support her point, Ocasio-Cortez shared an article about Kasich signing a pro-life bill into law. The law banned second trimester dilation and evacuation abortions. The article also mentions that "anti-choice extremist" Kasich actually vetoed a bill that would've outlawed abortion after the detection of a heartbeat.

Since running for president and running the state of Ohio as a Republican, Kasich has become a CNN contributor and endorsed Joe Biden for president. He's even speaking this week at the Democratic National Convention.

Despite all that, the exchange with Ocasio-Cortez serves as a reminder that dislike for President Donald Trump is not, on its own, enough to gain full acceptance or respect among progressive Democratic leaders.