OP, I can empathise so much with your situation, I've been there myself.
I used to really like and get on with my OH' s parents but when my dd was born they treated me the same way your IL' s are treating you and it annoyed the crap out of me. I will never forgive them for ruining my first week at home with my dd with their constant (although unintentional) overstepping of boundaries, interfering and stupid, ignorant comments. Gah!
I'd had a traumatic birth, resulting in an emergency c-section and had been kept in hospital for 3 days following the birth. I had been home with the baby just a day and a half when they decided to visit for the weekend. Bearing in mind that my poor OH had had no chance to bond with the baby and we had had no time to gel as a family, they turned up at our house that first day and stayed for nine goddamn hours!!!! Nine hours of them sitting here, expecting to be waited on with tea /food by someone who has just had major abdominal surgery, no offers to help out, watching intently while I struggled learning to feed my dd, making irritating comments about bfing "she's hungry again? Are you sure she's getting enough" etc.grrrr.
My mil would not leave the baby alone for a second. Taking her off of me, being constantly in her face, picking her up when we put her down, not handing her to me when she was clearly desperate for a feed (and that is really, really upsetting) etc. The poor baby got completely overstimulated by all this and decided to scream the place down from around 6pm to 1am as a result. Lovely.
Probably the part that most pissed me off though was my FIL refusing to give me the baby when we were eating and she was screaming for food because "Mammy is eating first and THEN you can have yours". Who does that? Who keeps a screaming newborn from her hormonal, lactating, frazzled mother? :-( luckily my bf stepped in on that occasion because I would have swore at him!
The second day - more of the same. They only stayed 7 hours this time as my OH ended up asking them to leAve (just before I burst in to tears from the stress of it all). The arseholes then decided to stay in town an extra 2 days (my OH got a little better at chucking them out when they got too annoying though).
Our relationship has just never recovered. I now just have this deep well of rage for my mil that won't abate. Everything she says just makes me want to strangle her. I have never felt as relieved as I did when they finally bloody drove off back home (with a promise to do it all in two weeks time :-( )
Yet I look like the unreasonable one because it all comes from a place of love for her grandchild (apparently - nth I still, to this day see no evidence of them ever putting the babies needs first, it's all about them). It would be so much easier if my parent in laws were just out right twats and I was ALLOWED to just hate them!
Sorry I've gone on a bit of a rant about my own experience there but I have kept all this pent up inside for almost an entire year and I finally saw a chance to let some of it out!
The only advice I can give you OP is to make sure you explain the intricacies of bfing to your in laws. I suspect that in your case, just like min, a lot of their hearty comments and behaviour around feeding the baby / handing baby to you are based in ignorance of bfing e.g. cluster feeding, building up milk supply, the let down reflex etc.
And deepest sympathies!