Personally, depending on my mood, if I have the obnoxious "sign in" prompt that medium and others give I'll maybe just not read the blog at all 1 time in 4. I am sure I am not the only one that gets put off by that crap.
Instead they have "pardon the interruption" and "Let's make this official". The "pardon me" politeness doesn't fly, because they recognize it as an interruption. If they are aware, then the polite thing would be to not interrupt.
And let's not make this official.
I don't want to sign up to read an article. I don't want the clap. I don't want to vote. I don't want to share my data. I just want to view the article. Maybe half way through I might even decide that the author has nothing interesting to say. 50% chance I don't want to read the full article.