"Genau wie X so Y" is absolutely fine, but is usually used with a noun phrase. This is the case when both parts have the same verb. It doesn't really work in your example, but it would be like this:
Genau wie die öffentliche Meinung über Politik so ist auch das Vertrauen in John Does Versprechen schwächer geworden.
But it's not restricted to a noun phrase and you can apply a whole clause as well, and as a matter of course you can then apply two different verbs. That means that your suggestion is OK.
However, in that case it's not uncommon to start the sentence with "So wie", as suggested in the other answer. And you can even combine both variations and say "Genau so wie...". In both cases you will often drop the "so" before the second part of the sentence. At least to my ear, a "So..., so (auch)..." structure doesn't really sound well in that case. But I'm almost sure others will disagree with me on this point.
For the sake of completeness, when the verbs of both clauses are contradicting each other (e.g. "more" vs "less"), then the sentence structure would be "So wie ..., so ist ...". (Here "So ..., so ..." is fine.)