Rudeness is culturally defined. People from different cultures (whether those are geographic, ethnic, or neurological cultures) have different definitions of rudeness. So the only logical way to define rudeness so it crosses cultural boundaries, is that it's deliberate, i.e. the intent was to hurt someone. Then the exact details of the situation don't matter, and it isn't open to interpretation, viewed through different cultural lenses.
Maybe if you said you didn't want someone at your party it would be because you didn't like them. But not everyone is you, so don't make assumptions about their motivations based on your own mind.
As it happens, she didn't like him, but there are plenty of people she did like and still didn't want to invite to the party. So the two are not necessarily connected.
I invited them because I happened to see them in person and the party came up, and the mother evidently didn't know what I was talking about, so I thought I must have forgotten to invite them, so I did. But then when I mentioned it to my daughter, she said she hadn't wanted to invite him. I get easily confused with in-person/verbal communication.
I didn't force her to have him there because I don't want to teach my female child that a male child's potentially hurt feelings (though I don't know if he even knew about it by then anyway) are more important than hers, and she should put them first, which is what women are taught to do in this society; prioritise pleasing other people (especially men) over their own needs/wishes. Having been born of an abusive relationship, this is particularly important for her.
The mistake was mine, not hers, anyway. It might be different if she'd invited someone and then changed her mind.
She'd already had some playdates with him and neither of them were enjoying it, so we stopped pushing it.