On top of that difficulty can be frustration when you pass the same gunk for days and sometimes weeks on end. What's the best way to address this when getting off your bike and removing the stuff yourself is not an option? Contacting the local Public Works department.
Many cities have a Public Works department that are in charge of street maintenance. This crew fixes potholes, helps with downed trees after storms and whose responsibilities are making sure things are running smoothly on the streets. They have an important, sometimes overlooked job of making sure that the streets and sidewalks are in working order so that folks can move around without problems or delays.
Some communities officially include reporting a bikeway maintenance or issue request as part of the mix of things that Public Works department takes on. In the City of Madison, Wisconsin, where I spent several years before moving to the South, there's a website that's used to report bikeway repairs. If you live in a community that has this kind of resource, report an issue the next time you encounter it and check out the response time. If there's not a system in place, call or email the local Public Works Director to let them know the issue. If the opportunity arises, see if setting up an electronic bikeway maintenance reporting website is a possibility. Chances are if you encounter a problem on a recent ride, someone else has dealt with the same thing.
I recently contacted the City of Clemson to ask them to consider street sweeping after a rain storm to address all the random sand, dirt, pebbles and things that had piled up in the shoulder. They did respond to my email, however, they said that the route I was on was a Department of Transportation road, and therefore, they weren't in the position to address it. Something about taking pride in the community, but it basically wasn't there role to stay on top of these kinds of things. (Another cyclist I knew reported things a few times, and got the same response.) Hmmm. Well, at least they are on notice that people on bikes are out riding and notifying them when issues arise. I suppose they'll have to work on the priority of addressing bike route issues, budgets and good PR.
After a ride, if there were some area that needed cleaning up, consider contacting the local Public Works department. Work with them to build bridges and help them understand the needs of the bike-riding community.