It looks like most don't because of both alleged Pagan harvest festivals being sacrilegious, and because it's a nationalistic/patriotic holiday.
SDAs (this year, at least) don't have a feast, fast, or holiday on April 7. https://www.adventist.org/en/information/special-days/ They do celebrate birthdays and are less restrictive about patriotic holidays than JWs, usually include some Christmassy and Easter-like things on the Sabbath closest to the holiday, etc. If she was vegetarian SDAs might be a more likely situation.
The closest I could find to an April 7th holiday is a Julian calendar Eastern Orthodox saint's day and then Lazarus Day on the 8th, but while my ex was Eastern Orthodox and celebrated birthdays (and so did his mother). As far as Paganism, the dates in general for March-May are March 21st and May 1st, none in April.
I can't find any Muslim feasts/holidays until later in April, or Jewish holidays before Passover, which isn't starting until the 10th at sundown.
I'm as baffled as you are unless your child is confused about the date and the other student was talking about today or another date -- today is the date of celebration of the Mormon church founding, and fundamentalist LDS sects are widespread and not all unde the Warren Jeff's FLDS sect. Mainline LDS have more holidays including Easter, Christmas, and patriotic holidays, but even in the pre-Jeffs era (probably more typical of other, non-FLDS fundamentalist Mormons today than the larger FLDS) they discouraged Christmas trees and birthday celebrations per Carolyn Blackmore Jessop's books.
If it's the 7th, I would suspect a obscure but modern fundamentalist Christian religious group that doesn't really do formal church but, like the Bill Gothard cult, instead focuses on having home churches.
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