Religious persecution, or overbearing regulations?

This certainly isn't a constitutional dilemma. But to engage on the merits...
The issue isn't what goes on inside your home, but instead the "externalites" that your meeting imposes on your neighbors.
When you live in a city with finite parking space in your neighborhood, your neighbors have a right to care about the cars parked on the street in front of their house.

If you disagree, then are there any limits? What if I want to hold a "Phish" concert in my backyard?

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Of course there is a Constitutional dilemma. You have a conflict here between freedom of religions/freedom of assembly and a city ordinance that restricts one or both of those rights. You might think that the issue should be resolved in favor of the city, but the dilemma is still there. There are questions here regarding whether this is a reasonable restriction of freedom of assembly and there will also be questions on if the city ordinance is unconstitutionally vague, meaning that it is so unclear that it violated the notice requirement of Due Process.