IIRC New Jersey revoked Women's franchise in the Jacksonian era due to perceptions of vote-buying and populism, and in the few cycles right before they did much larger numbers of women voted than had at first. If women keep the franchise, you could see NJ develop a much more populist political culture generally, or perhaps have some back and forth struggles over how to tighten or loosen the qualifications. If they keep the vote a bit longer, the start of national women's rights groups and organized women's political consciousness could see some of the early feminists and their abolitionist allies moving to New Jersey to take advantage of the vote. If that occurred in numbers, you'd probably see women's suffrage in NJ solidified, probably at least one 7 sisters type college in NJ, and an NJ that is a hotbed of abolitionism (otl it was lukewarm) in the run up to war. However NJ's politics work out, if it allows women the vote through the civil war then there's a decent chance of it spreading to other states during reconstruction. Kansas and New York, at least, had fairly close state-level contests on extending the franchise that narrowly lost; a functioning example to point to could well have tipped the balance. The 14th and 15th amendments would likely also be worded differently, though how would depend on the flocks of butterflies.