Treating things that are alike as equal.

Yes, it's an appeal to equality<>.

The statement: "This is some time [sic] a bought and paid for service that adults or adults and their children attend by choice." Is simply stating a claim that may or may not be true. We can only speculate. We need anecdotal or empirical evidence to determine the veracity of the claim. Is it plausible that adults pay for such a service for themselves and/or their children? Of course. We know of many instances where these (widely debunked) services are offered for money or sometimes simply as a prayer service. The claim infers that some adults and children attend by choice. Doesn't sound like a direct fallacy. There are many instances where children "volunteer" for such conversions. Overall, the premise of the question seems more of a form of hasty generalization, amphiboly, or just a poorly constructed sentence.

Was the argument further expanded upon? Because based just on that quote you appear to be making an inference that may equate to a straw man. "adults and their children attend by choice" states that the children are complicit in the choice, but this may be poorly worded and may indeed be a decision of the parents, but it doesn't say that, so worth clarifying (in fact what is actually stated is that the parents attend, which I highly doubt, casting further doubt on the wording). Even if it does mean that, it may still be worth challenging whether the children have any choice. Personally I doubt the children have any choice, but in terms of logic it's important to be clear on what is actually stated first, and then whether what is stated correctly reflects what the person intended to say.

Also once it's clear what is actually being stated, the veracity of the claim may be challenged, but that's not a matter of logic i.e. if the children are claimed to be complicit in the choice this may not reflect reality as the parents may be overbearing and the children afraid to challenge this, or they may not be overbearing but the children don't want to disappoint or go against their parents wishes or defer to their parents wisdom, etc.