I'm 32 years old and still live with my parents. Should I stay or move out?
We can't answer that. It's an individual decision. There are many such situations that are clearly mutually beneficial; there are many where dysfunction is perpetuated.
Some factors to consider are people's satisfaction with the arrangement; whether chores and expenses are equitable; whether the social lives of the family are impaired by the arrangement; health needs; economic options for other housing; and much more.
Most frequently, the situation is more complicated, with advantages and disadvantages. In such a case, you might benefit from consulting a personal counselor to review your options. You might also consider living independently but very nearby to maintain the positives of the parental connection.
It is also possible that you could try living separately with an understanding that all of you will revisit the situation after a period of time to see if that makes more sense than living together. In life, it is often quite acceptable and advisable to try out a situation before making a final decision.
We don't know enough to give you clear advice.