I was around back then, I remember the fight against it before and after its passage, and most importantly I remember that the actual legislative history of the Communications Decency Act disagrees with you. It was introduced by Senator Exon, a Democrat. Exon introduced it with a prayer that included the statements "there are those who are littering this information superhighway with obscene, indecent, and destructive pornography" and "Lord, we are profoundly concerned about the impact of this on our children." It initially passed the Senate by a vote of 81-18, with 1 not voting, and that 81 included plenty of Democrats. Then the Senate passed the conference version by a vote of 91-5. Bill Clinton signed it and made statements in favor of it, and his Justice Department vigorously defended it even as the courts tore into it.
People forget that in the 1980s and '90s, prominent Democrats like Tipper Gore were among the most vocal proponents of censorship.