In the context of people who were at a dance, 'to cut in on' probably means to interrupt a dancing couple by offering to take over from one partner. It sounds like Allie was wondering why nobody offered to dance with her. And she suspects it might be because people thought she was already married. - https://en.oxforddictionaries.com/definition/cut_in (the 4th meaning down) - https://www.macmillandictionary.com/dictionary/british/cut-in (5th meaning down) Hope that helps.

Hi, Mayllt. "to cut in on" means to interrupt someone who is speaking or doing something. Ex: Sorry to cut in on you, but there are one or two things I don’t understand. It's also possible to use "to cut in/to butt in" with the meaning of interrupting something: Ex: I'm sorry to cut in/butt in, but could you explain this a bit more explicitly? Lila cut in again, answering before he could even open his mouth. The same phrasal verb (to cut in on) can be used to describe a sudden drive in front of a moving car in a dangerous way Ex: She cut in on a red Ford, forcing the driver to brake heavily. I hope it'll help.