Admittedly I had the hardest time getting through TOS at first, in fact it took me years of just watching the 90's series (+ENT and the movies) and excluding TOS to make me realize that there are so many layers of references in the 90's shows to TOS that I now feel you can really miss out on if you don't watch it.

That being said, if I were a parent I would probably have taken the advice of a friend of mine who actually liked TOS more than the new series but wouldn't let her pre-teen at the time watch it. She wanted to wait until her kid hit the age where they could actually have a mature conversation about what was happening and put it into context. I understand the conditions the show was produced, more or less, despite not being old enough to see it when it first came out.

Honestly, all the Trek series to me have cringe moments, and that does not excuse them, but at least for me I like that I have identified them as problematic. Maybe by watching it you can remind yourself of the things you do appreciate about it and focus on how these relate to your appreciation of the later series.