Synthesis with input pin mode constrain

If you need the logic to actually change based on the input, then you don't want to tie it off, as you need the logic.

If the user knows beforehand which mode they will use, you would want two different configuration images, one that's high and one that's low, and be sure to give the correct one to the customer. As for that pin, if it doesn't do anything in the design, then don't put it in, and if the user's driving a device pin that doesn't do anything, be sure to assign that pin as a reserved input.

(You could also go more exotic, like having both images stored, and the user determines which image to use. They could drive another device that determines the config image, like a MAX device, or just have the device configure from image 1, and that image checks the pin status, and if it's in the wrong state it issues a reconfiguration from image 2...)