I'd have to see actual in-game examples for those moments to give a more detailed response. If you say "Lets get dragon" and the enemy jungler is up, and super fed... It would make sense why people would be mute, and do what they want instead. If it's the perfect moment for dragon, and they are still mute there's a good chance those 4 are in a voip call with each other. Sadly this game gets played by teens who think the world revolves around their group, and the randoms they get matched up with gets treated like an outsider, and in most cases an enemy. Nothing can really be done about that unless humanity grows up.
As for "Hey man, you need to do this" that's another thing I would need to see. If the person is losing lane to a bad match up chances are they are really angry already. Anything aimed at them will be read in an angry tone so I would just change up the wording, or just roam to that lane to help out (If you are sure it will equate to a kill).
Sadly sometimes though there's nothing you can do. People in this game become toxic over everything. Pre-Jhin buff's I was playing him, and winning every game. Ran into 2 people who decided to flame me because Jhin is apparently "a bad adc" in the champion select screen. Turns out... You can't even pick champs you are comfortable with/want to play in normals without being flamed some times. The best you can do is report them, and hope Riot looks through the material when the report gets viewed by a human's eyes. If a team is ignoring your attempts at communication there's very little that you can do. =\