SH mix 1to 3 h2o and some surfactant. put it on with a pack sprayer. let dwell 10 minutes minimum. pressure wash off at a medium pressure. Start with low pressure and increase as required but don't over pressure you will stuff the wood.
What is the issue with gaining access to the other side, bad neighbors? Anyhow,..not sure about fences,..but here in Pa I'm pretty sure there is a law that states a person has a right to property maintenance, giving access to any adjoining properties to do the maintenance.
Here's an excerpt I just pulled from a site called "bankrate"
Due to trespassing laws, you technically can't amble onto your neighbor's property without her permission. However, most communities have laws that allow you or your contractors safe and reasonable access to your property for repair or painting work. After all, most scaffolding is at least 4 feet wide.
Check into it's all you can do. Actually, I'd get your customer to do the checking and wait for their call.
I just did one of those, and the neighbor stood there yelling at me the whole time. Saying I was spraying harmful chemicals on his grass and in his pool. No matter what did he flipped out. Finally went and told my customer that I couldn't finish the job. She went over there and smoothed things out, I finished, but it was ridiculous the length I had to go to to clean a stupid fence. The guy actually went up on his roof so he could see what I was doing.
To minimize the chemical overspray you could use a paint roller and just roll the chemical onto the fence if you need to use chemical.
I have cleaned those kinds of fences with just water and they came out ok.
I would talk to them and let them know that you are going to just pressure wash the fence with water and because of the cracks between boards the water might get through to their side but it is only water and that will help their grass grow.
I am sure if it came to the police getting called, explaining to them that they are a problem neighbor and that you wanted to clean your fence, you explained to them that it is only water and that they still were a pita and called the police the police will probably understand as you are cleaning your property and not spraying hazardous chemicals over onto their property. Do they complain when it is raining? That is just water from up in the sky? I would tell the neighbor that one and see what they say as it is only water you will be using.
The white marks look to be from sprinklers, I would try to get them re-aimed or re-positioned before you wash because those stains will be back soon after you wash.