Technically, it does only say TRADITIONALLY... it doesn't say what you should do in an untraditional situation. So there's your loophole.
But if you were going to something like convention or State Day you'll only need your Phi Mu badge anyways. The problem probably mostly arises when attending campus events.
I know that other women on my campus wear their other "Greek" badges below their sorority badge because if it wasn't for their sorority they wouldn't be in the others anyway. So that is personally what I would do (although I ALWAYS forget to wear all my badges when going to anything
...)
As far as the tights/leggings are concerned, I know that some women would wear them to church and some would not. I don't think I would. My chapter simply states a dress code for their meaning of "business attire": dresses and skirts must stop no shorter than reasonably above the the knee and require stockings, no capri pants, full pants only, tops may not be spaghetti straps or clubbing attire (ex. "three finger" rule), no excessive cleavage, etc. This totally avoids the "tights" situation. (BTW-I love tights, I wear them at least 3 times a week but mostly at home).
Love you sis!