With all due respect I think you’re wrong.
Refer to pages 3 and 5 of the pamphlet you linked to. Basically it says there two points to consider:
1. A church can’t promote a specific candidate for office. This isn’t relevant here. In addition however, they can instruct their members about the teachings of the church and urge them to vote accordingly. For example, urging its members to not vote for pro choice candidates. They just can’t mention them by name.
2. A church can’t “devote a substantial part of their activities to
attempting to influence legislation”. This is the relevant portion in this case. The fact of the matter is most legitimate churches don’t spend the majority of their time attempting to influence legislation. Indeed, the churches in the Houston area I’m sure aren’t doing this. And haven’t done this.
There is a “test” provided on page 5 to examine this in more detail. However it’s on a case by case basis. Again though, even if the IRS were to peruse this action against the churches in question (and this is the salient point too, the IRS is the only one who can prosecute on such grounds, not local governments) they would have to show these churches attempted to influence legislation substantially as compared to their other activities. So at least over 50% of their time devoted to influencing legislation. Anything less would not be “substantial” by any reasonable definition.
I doubt those churches spend more than 50% of their time attempting to influence specific pieces of legislation. So their tax exempt status doesn’t prevent them from fighting against thus one ordinance.
How does a city mayor get to enforce federal tax code anyway?