Baby naming?

I really don’t know how to process this so I wonder what you all would do.

A coworker of mine happily told me that she (not Jewish) was having a baby naming ceremony. I was confused as she had never discussed being religious before but I know new parents tend to reevaluate so I clarified if she was having a baptism or other religious event for her to share about. She then said no that she wasn’t religious and didn’t want to fuss with finding a church to attend but did think she would want a ceremony. She said she was very inspired by my description of my child’s Brit Milah and was going to “do the same thing”.

This was very shocking to me and I clarified it would not be the “same thing” since the Brit milah is an ancient rite for Jews and not a sip and see or open practice for others but that there are different cultural practices that are specific to her backgrounds traditions that would be appropriate and perhaps she should find value in those.

I think I was mostly triggered by her saying she was going to do “the same thing” and feeling like her baby celebration, while valid and important to her and anyone that wants to show their love to her new family is somehow equal to the grave responsibility and honor it was to welcome our child into the covenant or that there were elements of the Brit milah that are “universal” to non religious people to welcome their child into their “tribe”. But am I overreacting?

I am unlikely to seek to discuss further since there is a time and a place for discussions around religion and I feel I’ve learned a lesson. But I think I am especially hurt because I was happy to share memories and my experience about such a special day that I agonized over and what I saw as real interest in discussing my culture. now I feel betrayed that my sharing has led to such appropriation. But am I overthinking, maybe there is an element of the baby naming ceremony that is common to all cultures and not necessarily following its order provides an authentic meaning for all people?