I haven't seen any issues with the correct BB sway bar, I have an aftermarket and a ton of room on mine, and used a factory CJ with the T-pan as well prior to the big bar
As you pointed out, not all bars are the same, my guess is yours may not be the best fit for a Mustang. I do agree it should be as straight in each direction if you can, but in use, it's never straight or aligned, the bar ends and lower control arms all travel in different arcs
Also, the sway bar mounting location doesn't affect alignment, in any way The upper arms are fixed, the lower arm is located by the strut bars and the frame mount, the only thing moving the sway bar (assuming you needed to) would potentially side load the sway bar end link itself