I've never really had any major issues with anyone, each to their own, and as long as they are not physically hurting or endangering their kids, it's not really our place to judge.
In saying that, DP lost one of his lifelong female friends over parenting styles. She and her family moved a long way away, but they were always on the phone to each other, and we would see each other a few times a year.
Their DS1 was a year older than our DS, but much smaller. Whenever we saw them he would try to bully, push, pull, hit our DS, but our DS is such a laidback little guy he would mostly ignore it, but a few times he did hurt him, and she never noticed. More than once I picked DS up off the floor when he was learning to walk after another shoving onto polished boards or a slap or punch. I told him off without hesitation, not harshly, but so that he knew it was not right. When they had another DS he picked on his brother terribly, one time when we went to see them he pulled the 6 month old by his head along the floor.
Then for some reason, she decided to start telling DP whenever they were on the phone that his smoking (he smokes, not in the house, not around the kids, has a jacket that gets left outside, brushes his teeth after. It's not ideal, but you can't force someone to give up) was damaging his child, he was an irresponsible parent, his son was going to grow up to hate him, all this stuff.
DP doesn't normally take that sort of critisism well, he prides himself on raising a well mannered, thoughtful (as much as a child can be lol) intelligent boy. They go for walks, to parks, read, play together, make things, cook, and spend quality time together. I have whinged a bit about DP in another post, but like I've said, I know the stay home parent has a hard job, and DP always makes sure he has time for the kids during the day to have fun.
He finally had enough one night when she was having yet another go at him and told her he thought someone who had raised a mean little bully shouldn't be judging our child by what his father does, and because he smokes doesn't make him less of a parent. Then he told her all the things her son had tried to do to ours when they were playing together. She got hugely offended, and told him if he'd said something at the time she would have done something. To which he replied she was there the entire time he was, if she couldn't see what her son was doing it wasn't his job to teach her how to parent.
I probably wouldn't have worded it that way, but he'd had enough. They have barely spoken since. I'm friends with her on FB, but she hardly talks to me either after she had a rant at me about how wrong he was and I wouldn't join in lol.