OP you sound lovely - you came to ask for constructive feedback, took it on board and are going to use the advice going forward. What more do people expect? It's nice to see so many replies that are supportive but sad that there's quite a few people who "can't understand" how OP has gotten to adulthood without having the exact same experiences they have.
OP does know that gift giving is a "thing" at parties but explained that she thought it was specifically about getting something nice that they liked and therefore did not understand that it is the social norm to get gifts for people who are essentially strangers. Why is that so hard to understand? From the sounds of it, OP didn't go to many parties as a child due to social issues and presumably as an adult she only attends events of those she is very close to and therefore would buy a gift for anyway.
In fact, does anyone regularly end up at strangers' parties as an adult? This seems like a primary school thing, where everyone gets invited. As you get older, parties get smaller and if you end up being invited to someone's party, you probably know them at least reasonably well. How would OP be expected to know the etiquette for "parties-where-you-know-nothing-about-the-person-but-their-name?"
ND people don't see things the same way as NT people and so don't always pick up on unspoken social rules or understand how social rules in one situation are generalised to others in the same way.
My DH and I are both ND. I can easily see my DH not knowing to bring a gift. I would have known to bring a gift but I would potentially have struggled socially while actually at the party. And for the record, we didn't elope to get married but we still had a small wedding with only immediate family. Not everyone has a big wedding and those who struggle with sensory and social issues may be even less likely to.
The woman who said all of this to OP is a horrible bully but I'm not surprised. There is a joke that school bullies should be used to help diagnose autism because they can basically sniff it out. And in my experience, not only is it true but it doesn't stop with children. Adults are generally much nicer but there are still some adults, like the one here, who are downright nasty bullies to ND people. Imagine saying all of that to someone, unprompted and then scoffing and adding that OP doesn't even know how to dress appropriately? It's like something from a teen high-school film, but unfortunately I do believe it's happened based on my own experience of people like this.
My advice to OP is to try to remain reasonably civil yet distanced from these horrible mums and try to figure out if there's some nicer mums in the class who you could invite to play with your DD? Yes, you are going to have to be around these mums for several more years, but I don't think twisting yourself into knots trying to be friends with bullies is necessary. There's strength in numbers and if you can find a few parents and kids who you and your DD can get along with then it will make things much easier.