with respect to a State or local income tax imposed for a taxable year beginning after December 31, 2017,
Doesn’t talk about property taxes. In my case, I receive property tax bill in Sep or something like that with 1st installment due in Dec and 2nd in April. I feel comfortable in paying off my April payment this year and claiming it on 2017 taxes.
However, in some states (at least) you can pay more estimated 2017 taxes today and carry over any overpayment to 2018 on your 2017 tax return. Technically, that wouldn’t seem to be a prepayment, rather an overpayment since when you make the payment you are designating it as payment of 2017 taxes (it is “with respect to 2017” when you make it). I live in NY and it appears that the NY tax form IT-201 has a line entry to carryover an overpayment to the following year, and you can pay estimated taxes online.
Really speaking that is a refund that you are electing not to be refunded. You will get a 1099-misc for that extra payment anyway. This is exactly what the “text from conference” that you highlighted is trying to preclude. They don’t want mega-millionaires to go pay all their 2018 state taxes on Dec 30th, 2017.