Yes on registration. Does your state use sale price or MSRP for sales tax? Mine uses sales price for sales tax and MSRP for registration, in which case my sales tax would not increase but my yearly registration would be increased, in my case in a 10yr span that might total $200-300 more so a little bummer but not kick in the balls. Interest won't really be much more since sales tax wouldn't be up, and my first year of registration would be up <$100 if that was rolled into a loan, meh. BUT if you mean the fact interest rates have risen at least 1% and are continuing to climb over these months... yeah that's gonna pencil out to a couple grand or more in interest which does suck.
Ford could offer 2-2.5% interest loans on all these orders to mitigate the increased interest rates if they wanted to make up for the delay... don't hold your breath though.