I know a lot of people who vote without even really reading what’s on the ballot. They just go with whatever option has D next to it. Others do the same but for R.
Personally I can’t vote so it’s mostly an interesting phenomenon to observe
To attempt to be helpful, I’d suggest that what you’re referring to is more of an issue of uber partisanship than identity per se.
You can see this in how people say “I am a democrat/republican”. They don’t say vote or belong to or member of, people very explicitly talk about it as an identity and both or all parties encourage that.
The Ds assume I'm an R, and the Rs assume I'm a D. My voter registration says "Pacific Green" and I vote Green/Independent most of the time when possible.