It really depends on the land owner as the farm owners also own the dikes (crazy situation considering the dikes were built and are maintained with public funds). Places I know neither the land owners or city employees I have encountered ever say anything about it being private or ask me to leave. I have been going to some of those areas for 60 years.
I believe the area from the bridge over #10 to the canal just south of 64th is accessible to the public as is the east bank from the canal confluence to 64th.
I think the city is posting those dikes because they want to avoid any liability if anyone experiences "misadventure" or other mishaps. Some of the coyotes in Surrey are starting to grow pretty big!
There are have been parking issues with some access points on busy roads which may explain the fences. I have been waiting to see if those get erected across some of my favorite spots.
BTW you can use use Google Earth to see if fences and gates have been put up at many crossing and other access points.