Hmmmm...didn't somebody have a documented, step by step process as to how certain threads unfold sometimes. I think we're on about step 3 but I'll give it one more shot too.
Still, I came here because I think there are probably some dogs that can be persuaded or avoided.
Michael, no one is denying the fact there's a problem out there. Unattended dogs can and will chase bikes. And it shouldn't have to be your responsibility to persuade or avoid them. Using sound devices or bear spray can certainly be a deterrent in a lot of cases but so can simply removing the chase.
I don't believe there is a lot of productive training or even simple management going on with these so called "protected religious figures". And OMG - did someone actually describe their dog that way to you or is that another one of your interpretations?
In any case, each time a dog is allowed to chase a bike, with the chase successfully ending in the bike leaving the vicinity (which is going to happen every time), their actions are reinforced. They know what to do next time they see one - chase it and it goes away. It's a quickly learned bad behavior. Stop the chase and most of the intensity in the situation is removed.
Of course each situation is going to be a little different and it would depend on the dog and your skill level as to how it could be handled. I don't know you and think it would be irresponsible to even recommend carrying a stuffed toy to throw at them at this point.
You're looking for a bullet proof solution that will protect people in all cases. Do you think recommending bear spray or weapons to children is a viable solution? There's a certain amount of training involved in the use of these tools and not everyone is capable of using them effectively, often to the result of being harmed by their own actions as opposed to any real threat the dog may have presented.
The dogs need to be trained not to do this and it shouldn't be your responsibility to do that. It's the responsibility of the lazy, irresponsible owner. This is where your challenge is.
It's easy for these owners to say, I didn't know he did that or he's always liked chasing bikes, I don't know why he does it but he doesn't hurt anyone - totally removing the blame from themselves. This is where they need to be educated. If you don't feel you can reason with them, hit them in their laziness and apathy towards taking ownership of THEIR problem. Bring that to the politicians. Remove the blame from the dogs and place it where it belongs.
In that ownership and really looking at where the problem lies, who has an ability to fix this? It's not me, it's not you, it's not the politicians and it's certainly not the dogs - it's the owners of these dogs. They are the only ones that truly have an ability to make the solid changes these situations require.
Don't portray them as ruthless thugs or a new segment of society that enjoys harassing leisurely bike riders with scary dogs. This may be the case in the odd situation but for the majority of dogs out there, there's simply an irresponsible owner in the house that's not properly exercising and containing their dogs. They're letting THEIR laziness dribble out onto the street and causing discomfort for law-abiding citizens that want to use it. That's what needs to get publicized.
Lazy, irresponsible owner allows "protected religious figure" to run free around neighborhood.
Lazy, irresponsible owner is not exercising their dog and forcing the bike riding public to train their dogs for them.
Lazy, irresponsible owner is exposing their cherished pet to harm by allowing them access to play on the roadway.
If it's a group think on an entire street, publicize that street as having a bunch of lazy, irresponsible owners.
I don’t think I'd go so far as condemning the whole of NE Texas (that's a pretty big state with some pretty liberal laws and that would just be wrong); keep it truthful and local where the problems are directly affecting you.
Get enough of that out there, maybe even with some names attached, and I'll bet you'd start to see some changes.
If you think you're dealing with big, dramatic "egos" (they’re obviously playing with yours....)
.....you must be a creep or something
aim some well thought out, harmless but piercingly productive bullets straight at those egos.
The dogs have NO ability to comprehend what you're upset about, the owners do.