The thing is, ubiquitin, that the minhag isn’t really so similar: the dough is merely pierced with a key, and another form of the minhag is just shaping the dough or some seeds like a key. Also, who’s to say that the christians didn’t get their idea from us? And not all similar things come from one another; for example, some old haggadas have a picture of a rabbit by yaknehaz, because “haz” means hare or rabbit in german or something like that (at least, that’s what I’ve been told.) But would you suggest that due to the proximity in time of pesach to lehavdil easter, it means that the rabbit was taken from the christians? Of course not, because we have a separate reason to explain the rabbit, or in this case, the key.
And. when you say that yidden make schlissel challas specifically this time of year: it’s true, but the time of year is the source of the minhag. At least one explanation is that the key is to remind us that we have the “key” to unlock great spiritual achievements in this great time leading up to matan torah.