This has been a fascinating, and long, read!
My fundamental opinion: being a parent to a toddler is, at least some of the time, extremely challenging - however you choose to do it. (I don't think I've ever met an 'indifferent' parent - in one of my many judgemental moments I may think I've spotted one in public, though I actually believe it's fairly unreasonable judge without getting to know at least a few things about that parent's life).
In terms of the OP - it sounds like a really difficult situation that you're in. Even though others on this thread (myself included) can clearly relate to that feeling of diverging from your friends on parenting issues, it's probably impossible to give really helpful advice without knowing a little more background (which, understandably, you might not want to provide) - like how long you've known each other, and what kind of social support you yourself have.
My own advice would be to try to talk to your friends as individuals rather than in a group to get a sense of how possible it might be to change the current situation. Perhaps on neutral territory like in a cafe or, even better, on a walk - something about being outside often helps with emotional conversations (I think). If you were able to get a conversation going about, say, comparing notes on what you each found challenging about parenting, that might help pave the way for doing things differently in group situations. Or you could simply say 'I find it difficult to know what to say to my son about why he's not allowed to do things that your child's allowed to do - is it possible for us to agree on a few ground rules for play dates?'.
With your 'extended breast-feeding friend', I personally do not think it's unreasonable to feel annoyed/ overburdened by hearing about an unchanging situation so often - it's not as though you've described saying/ doing anything to her as a basis for your feelings (which could be then labelled as 'reasonable' or 'unreasonable' by others). I'd hope that all the 'gentle parents' out there, who are probably generally fairly concerned with validating feelings in their children (whilst aiming to moderate actions) would extend that same courtesy to fellow parents. I personally am a great fan of the importance of acknowledging feelings, but would never in a million years call myself a 'gentle parent' - it seems to stray far too close to suggesting that many others are 'ungentle', despite providing stable and essentially loving homes.
I would aim to, again, have a one to one conversation with your very sleep-deprived, nipple-chafed friend, and say 'it looks like you're going through a bit of a hard time of it at the moment'; then encourage her to talk about things at as much length as she can - without giving any advice. Often, by talking through their own problems at their own pace (given enough space to do so), people come up with their own solutions - these tend to stick much better than the best possible advice from others. It might also mean that she mentions it less from that point on - this also often seems to happen quite a lot after people feel properly heard.
Huge luck to you. Trying to change the dynamic of a group that you are in is incredibly hard, but can be possible - we are more than just members of tribes.