When I was a young adult (18-20ish) I road a bicycle out of necessity. Was too poor to buy a car. Had one briefly but it blew a head gasket and I wasn't familiar enough with how to repair it by myself so the repair took nearly a year. So I had to ride around Houston to work, shop, etc. My longest ride was a challenge with a friend, we road 50 miles in one day, along a freeway out of Houston and to the North to Cleveland. We stuck to the shoulders.
That said, I know how crazy it was to ride in areas where there is traffic, and only a narrow shoulder - or no shoulder. If a cyclist is riding for FUN or EXERCISE and not out of NECESSITY (transportation), they need to stay off of certain roads, for their own safety. It's not about "rights" it's about "You're going to end up injured or dead" because there's either going to be some yahoo checking their cell phone that doesn't see you, or some red neck with anger management issues.
For example... there's a highway through the woods in my area. One of those highways that really hasn't changed much since the 50s except a few extra layers of blacktop, and the trees are cut back a little farther than they used to be. I had to take that route as a detour recently. 65 mph, some sections straight as a board, others winding through the trees. No shoulders. And wouldn't you know it, ran across a group of 4 cyclists getting in their miles. I would NEVER have even considered that when I was cycling as a young man. Your only escape route is the grass. So of course, there was a line of cars stuck behind them in a 65mph zone, piling up, until finally a straight section with no oncoming traffic was reached and you could brave passing.
Same area, btw, where this happened just last year (and you can see what kind of road it is):
Driver walks free after hitting six cyclists, killing 1 in Liberty County
I bear no ill will to cyclists, and I understand they feel they have a "right to the road". However, they need to leverage that right to get proper shoulders and bicycle lanes built, and not to use mainlanes on high speed highways.