Oooh this is a good topic! Thank you for bringing this up; these internal scripts can be so difficult to address and it can be intimidating to talk about.
I think that if we have any insecurities around appearances in our own lives they tend to be amplified a thousandfold as parents. I have two really close friends who have young kids and the mom-shaming culture seems to be waaaay more prevalent than when my son was young (before Instagram or Pinterest existed!). The external pressure to do things like theme birthday parties for infants blows my mind - that just was not a thing where I lived.
I consider myself lucky that I had little money when my son was young and we moved to Minneapolis; there was no way I’d be able to buy the strollers that were all around me at the park so I simply wasn’t bothered to compete. I got a lot of rude comments from moms but not once from a dad, if that doesn’t say something about our culture. I’m not overly conscious of branding or how I come across to others based on my stuff - but my brother always was, even when we were young, so I can empathize with that mindset.
You know the trite saying about attractiveness that indicates confidence is more importance than what we actually look like? I have found as I’ve gotten older this is true in all areas of my life, especially around parenting choices.
Where you live and the cultural expectations around raising kids can definitely affect your self-confidence or insecurities/anxiety. Getting past the shame spiral won’t be a simple mental switch that you can turn on/off; but a practice.
What will work for you will be individual to you - but maybe start with reframing your purchasing decisions as a positive thing - memorize @Smacky’s words and tell them to yourself whenever you start to feel self-conscious around other moms “Spending less for a perfectly good carseat or having a not fancy but functional stroller are reasonable and smart choices. Why pay more for appearances or for some idea of what you should be doing?”
Another key piece is finding like-minded people to talk to and celebrate your frugality with, to counteract the narrative that you “need” certain brands. That’s us! When I first moved to Minnesota I would have lost my mind without an online parenting forum that was aligned with my personal values, to reassure me my kid would turn out just fine without playing hockey by age 3. It can feel very isolating being surrounded by people that think differently than you.