How do I divide a 1x6 equally to make two 45 degree edge French cleats?
You don't have to divide the board equally to make workable French cleats.
If you need to do multiples that match just pick a fence position that approximately divides the boards you're starting with, write down that setting so you don't forget it, then rip each subsequent one the same as the first. Attach the same wider or narrower piece to the wall each time.
A 1 x 6 will be 3/4" thick. A 45° cut will have an offset of 3/4" for placement. Half of that is 3/8", which will provide for the duplication you seek. Locate the midpoint of the board, move the line by that amount and make your cut. Obviously, you'll want to ensure that your angle is tilted the correct direction. In this case, it's measure twice but also check your triangles, then cut once.
Not to scale, but pretty darn close. The saw blade should be centered on the line in order to balance the kerf material reduction for both sides.