My fiancé's parents want to ban kids, for seemingly no reason

I would definitely let it go for the time being, considering your guest list won't have to be finalized just yet. But if it's still an issue when the time comes, I would have your FH tell his family that you want to have children at the wedding. If that's an issue for them, I would respectfully decline their offer to pay for the food for the wedding.

I would say that maybe they want adult time only. I know I plan to have a post elopement party adults only except my nieces and that is only because my sister in law lives out of state and won't travel without them. I think receptions adults want to drink and let loose and I know I feel odd doing it around kids and feel like I need to filter myself. Did you ask them why they felt that way if money and space isn't an issue? Ultimately it is what you and your FH want.

It sounds like you want to invite kids, so invite them your in laws will get over it!

I suspect they don't like having kids at a wedding, and are using the fact they are paying for the adults at the wedding as leverage to keep that from happening. So you may end up having to figure out whether you are willing to pay for the whole reception (not just the kids), or comply with their demands.

But you and your FI need to get onto the same page about this. "My fiance doesn't care either way since he's not paying for the food" isn't really a good answer. Would he like to see his cousins' kids there, or would he consider them a distraction if one of them cried during the ceremony, or if adults on the dance floor were tripping over one of them? The two of you need to make a combined decision, and then he needs to be the one to convey it to his parents. It is way less likely to cause drama if the one conveying the news is the one who is related to them, and can say, "Jasmine and I are agreed that..."