That's a common myth, and is completely wrong. In fact, it is almost 180 degrees wrong.

Before section 230, there had been a couple of court cases. One held that a particular provider was not liable for anything posted on it, because it did not do any filtering or blocking at all. Another held that a different provider was liable for what users posted, because it did do some filtering and blocking.

Congress felt these outcomes were wrong, and section 230 was specifically meant to make providers not liable for user provided content, regardless of whether or not they did any filtering or blocking.

And yet sites that aggregate illegal content are taken down by the government all the time, despite hosting none of it themselves. If you filter the wrong way, the government will hold you liable.

The Twenty-Six Words That Created the Internet:

"No provider or user of an interactive computer service shall be treated as the publisher or speaker of any information provided by another information content provider."

-Section 230

[1] https://www.amazon.com/Twenty-Six-Words-That-Created-Interne...

This podcast goes into a lot of detail on what the CDA says: https://legaltalknetwork.com/podcasts/make-no-law/2019/08/de...