Allow me to publicly follow someone while privately ignoring them. Allow me to easily and permanently get rid of "In case you missed it" thing and read my feed

Allow me to publicly follow someone while privately ignoring them. Allow me to easily and permanently get rid of "In case you missed it" thing and read my feed on a strictly timeline basis. I get a lot of junk in my feed that I don't want to see, and thus I don't go to it much. Facebook is not as bad, but they've gotten worse. Two of my friends "like" some newspaper and then I start seeing the latest stories from that newspaper in my feed all the time. I want to go to these feeds once a day and read what those who publish once a day or less who are my friends (Facebook) or friends/colleagues (Twitter) say, in timeline order. Any deviation from that lessens my desire to read it. Some of my friends publish to Facebook several times a day and I usually don't even want to read that, never mind the other junk that both put in my feed.