Bf is entirely normal.
However it does involve some exposure if you're not adept, which is usually when you are at your post natal, baby blues, body feels battered and scarred phase (for anyone about the shout me down I'm a natural term breastfeeder of a 2 1/2 year old who ran the local NCT cafe for a while too. I have seen many women learn to feed their first. The no one noticing/no one ever gets squirted comes a month or two down the line). That's aside from any cultural issues or other unsupportive people on that day.
Not every feed needs to be a political act.
A woman's right to feed does not come with a caveat "but only if she wants to fight for us".
A woman can be shy, or apolitical or gasp just not give two shits about the rest of us feeding and she still absolutely has the right to breastfeed as she wishes.
Therefore rooms may be offered but not forced. There isn't a problem with that.
The Badass Breastfeed did a fabulous post about breastfeeding mums who use a scarf or cover and why no one has the right to criticise.
I had a disgusting pupps rash when I first fed - wanted to cover that not my boob. I have over supply and uncontrollable let down. I used an apron and found I liked it because it also helped dd sleep - comments as if I was "ashamed" did not go down well.
Expecting all breast feeding women to be strong, public and fighting for it actually de-normalises it, by alienating a huge swathe of people who just want to feed, and find the idea that if they cover etc they are doing it "wrong" (if you ever think/say that, you are a stone cold sanctum bitch and need to check yourself - that is not lactivsm but one up woman ship) isolates them.
In the cafe/support groups I went to and volunteered at this came up again and again.
The act of accepting the shy feeder is an act of lactivism - at the same time as ensuring rooms, covers etc are not suggested or forced.