Was David Jewish??

This is the most fundamental question, and it must be addressed. Why is there a doubt you ask? The answer is because it says in the book of Deuteronomy, Chapter 23, 'An Ammonite or a Moabite shall not enter the congregation of the L-rd, even their tenth generation shall not enter the congregation of the L-rd, to eternity, because of the fact that they did not greet you with bread and water on the road when you were leaving Egypt.'

Furthermore, according to the last verse in the book of Ruth, David's great grandmother was Ruth, a Moabitess!! How could Boaz be allowed to marry Ruth when it is clear that Ruth was from the Nation of Moab? Any thoughts? I would love to hear from you.