I have attended the Mardi Gras festival in 'Nawlins' (New Orleans) all through my life, so this answer is derived from personal experience rather than facts. My experience has mostly been as a "bead provider" on the "supply side", but I have also attended with my wife and children along with coed groups.
To my knowledge, "breast begging" at the festival has been a matter of 'cultural gravitas' that has been going on for a long time. There is a brief vignette of it in the film Easy Rider (1969).
I have been in discussions with so-called 'Dylanologists' who claim that there are shrouded references to this aspect of the festival in the lyrics to Mr Tambourine Man, which would date it back to at least 1965. The only comment Dylan himself ever made about the song is that was inspired at the Mardi Gras and it's not about LSD.
For those not familiar with breast begging, the males will pitch beads at the women who pull up their tops to reveal their breasts. The women collect the beads and string them together into a necklace as a sort of 'badge of honour'. It is the never-ending cat-calls of encouragement to the women that some find intimidating and I suspect this intimidation forms the motivation behind your question.
I would like to ask a question here for her, is it normal to walk on main Bourbon street for a girl and not to exchange beads?
Define 'normal'. There are families with multiple generations out on the streets enjoying the cuisine and music, including grandmothers. There are also holy-rollers, bikers, evangelicals, street bumpkins, goth punks, meth dealers, gawking tourists from Europe and the Far East, and nearly everything else you can think of. They ignore that part of the culture. Once the lads see that you are not a 'player' they will generally leave you alone. HOWEVER...
Without doubt there is a subculture on Bourbon Street during the festival can be interpreted as misogynistic. It's frat boys and rednecks and roustabouts and similar groups of young men who are out on a lark and there's enough participation from the female side to keep the tradition alive. There is too much momentum to the tradition to think it will stop in 2016 just because times have changed. The cat-calls and raucous leers are going to happen whether you like it or not. If you think you will be overwhelmed by the intimidation, don't go.
On the other hand, there's a great piece of advice for dealing with the breast begging subculture: ignore it. It's meant playfully and nobody will assault you or abduct you; and the police will intervene if a given crowd gets too rowdy. Just ignore it. Mardi Gras is a great festival and a piece of beloved Americana; it's an all-around jolly hoot and there is no reason to avoid it because of the breast begging subculture.
