I don't want to tell my parents about a show I'm doing.
Why don't you want to tell your parents about your show?
My parents are conservative about my career. And they are not supportive of my unconventional style of doing art.
It's fine for you to not tell your parents about your art show if you aren't comfortable doing so. Not everyone needs to know about every aspect of your life.
I think they should know since I'm their child and their son.
I expect you don't know everything about your parents and you are an adult so it's normal they won't know everything about you.  You shouldn't feel obligated to tell them unless you actually want them to know.