You may be too young to remember, but this was frequently an argument over Usenet censorship during early-to-mid 1990ies — that by censoring some posts an ISP may lose their Common Carrier status and have to sensor all posts from then on.
You may be too old to remember, but ISP's were dragged kicking and screaming into being classified as Common Carriers just last year. The FCC forced this status upon them in order to enact net neutrality rules. I'd give you a link, but you helpfully already did...see the last sentence under "Telecommunications".
In the early to mid 1990ies, ISP's most certainly did not have common carrier status.