Hello Miguel
Although I do not think dogs are the cause of the skin rash problem experienced by some (just an unfounded opinion), I do share your concerns about dogs (and babies) in the pools having the potential to pose a health risk to soakers. Another potential problem is human waste that is often left too near the stream.
Deep Creek Volunteers provides "hot springs etiquette" tips as a part of our brochure which is handed out at the springs and also made available at Bowen Ranch. We suggest keeping dogs out of the pools as well as owner monitoring of dogs to prevent them from disturbing others. (We also give appropriate instructions for human waste) While we have no enforcement powers, I believe that our suggestions help to keep the idea of responsible hotsprings use in enough visitors' minds to make a difference.
DCV also encourages others to speak up for our standards while at the springs. When a visitor or group, through disregard or ignorance, acts in a manner that causes a problem, the situation can often be remedied by other visitors, and especially by groups of people. Not all people will change their behaviors when others suggest it, but many will, especially if they feel that they are in the minority.
For a practical way to avoid problems with the skin rash, keep your ears above water in the hot pools and avoid long soaks, or vigorously towel off after long soaks. (this has worked for me)