Let’s consider how one would “follow” false doctrine on social media. Are you paying close attention to the promotion of false doctrine on social media, as in “I’ve been following this Facebook discussion about Calvinism very closely”? If so, why are you paying close attention? Is it because you recognize the biblical truths which contradict Calvinistic tenets and you wish to share them with the participants of the online discussion in an effort to bring them to the truth (2 Tim. 2:24-26)?
If so, that’s certainly proper since you’re working to expose error and speak the truth in love (Eph. 5:11; 4:15). My only advice is to do so with tact, patience, and wisdom (2 Tim. 4:2; Prov. 15:1; Matt. 10:16), recognizing whether to continue the discussion if you see you’re dealing with someone with an open, honest heart (Lk. 8:15) or end it if you’re dealing with someone with a hard, closed heart (Matt. 10:14).
Are you following the false doctrine online in the sense of conforming to it? If so, that would be a grave sin that would put your soul in danger (Rom. 16:17; 2 Pet. 2:1-22; Tit. 3:10-11; 2 Tim. 4:3-4; Matt. 7:13-27).
It would be much better to have the mindset of the Bereans, whom God considered to be “noble” because, after hearing a man preach, “examined the Scriptures daily to see if these things were so” (Acts 17:11). Treat any theology that is promoted on social media as you should with the theology promoted in this Q&A forum and any sermon, Bible class, blog post, article, or book…by testing it against the parameter of rightly-divided Scripture in its totality and choosing to “hold fast to what is good” (1 Thess. 5:21; 2 Tim. 2:15; Ps. 119:160).