Maybe progressives support net neutrality because they see it is a way to get the government more involved in regulating speech. They could see it as a path to eventually banning hate speech, or banning the ability for Christians to proselytize. And that is a legitimate concern. Also, allowing the FCC to implement it unilaterally is problematic. That said, maintaing unhindered access to the internet by anyone is also of paramount importance. It could all end in a giant liberal/google run oligopoly otherwise.
Net neutrality was never about “unhindered access to the internet” anyhow. The more control you give to the FCC, the greater the liberal influence.