No, because they can afford the legal fees. It will be worst for smaller sites. From the article:

With Section 230, if a website (or a user!) wants to defend its right to keep content up (or take it down), winning such a case typically costs around $100,000. Without those protections, even if you’d ultimately win on First Amendment grounds, you’re looking at about $2 million in legal fees. For Meta or Google, that’s a rounding error. For a small news site or blog, it’s potentially fatal. And this includes users who simply forward an email or retweet something they saw. Section 230 protects them as well, but without it, they’re at the whims of legal threats.