Does an HOA in a still developing sub-division in Thurston County, WA have the authority to fine homeowners for street parking?

It depends on several factors. If the streets are dedicated to public use then I don't think the HOA can prohibit parking. But if the streets are in fact private ways within a development, the HOA probably can set rules concerning parking on them. In order to figure it out, I think you'd have to look at the plat, the HOA's governing documents, and the CC&Rs for the development. Somewhere within those documents it should state, expressly or impliedly, whether the streets are dedicated or if they're privately regulated.

I agree with the two prior answers, but I would add, it may also depend on your HOA agreement. They may have some additional rights, and if they do, even if they are wrong, you may be in a tough legal battle. HOA's often also arbitration clauses, and in my experience use them to overstep their authority. If you cant live with what the HOA demands, I would recommend that you look to moving.