And honestly m_stapp... you were given the correct answers.
You have to search to find what you're looking for. It's right there in the statutes. Chapter 452.
Your original question wasn't worded to be interested in ideas or theories. It asked a direct question, for which you received direct responses.
"If a mother and father are not married when a child is born, which is more and more common, if their is no court ordered visitation does the custodial parent have to allow the non-custodial parent visitation. I know they both SHOULD have the same rights to parental relationship but do they?"
That was asking for a direct answer, not opinions.
You weren't GIVEN a direct answer, because you've made your reason for being here known. You're in school and researching. The people on here help those who are actually facing these situations, not some hypothetical posed to you by your Civil Lit. teacher or something.
I have, however, told you where to look to find your answers. In the Statutes for Missouri. Even told you what chapter to look in.
The rest is up to you.