You can already sue them. For example, if Fox runs a segment claiming that you (gulli1010) are a murderer, you can sue them for slander (with or without this executive order).

If someone tweets that you are a murderer, you can't sue Twitter (or rather, if you do, Twitter will be protected by Section 230).

However, suppose Twitter announces the following policy: "Any tweet which calls someone a murderer, shall be deleted, unless the alleged murderer is gulli1010". Should you be allowed to sue Twitter then? That's a more nuanced question. And what if the above policy isn't an official policy but is a de facto policy?