These certainly are important, and I'm thankful you have high standards for a future husband. Far too many young people, I'm afraid, enter marriage hoping their spouse will change and become a better person afterward but unfortunately, it seldom happens.
At the same time, however, I hope you also will listen to your parents and then set an even higher standard for your future husband. They know that spiritual unity is a very important part of marriage and if it is missing, your happiness will not be complete. This is one reason why the Bible warns, "Do not be yoked together with unbelievers. For what do righteousness and wickedness have in common?" (2 Corinthians 6:14).
I can't help but feel, however, that you are actually facing an even deeper issue and that is your own relationship with God. Perhaps you believe in God; you may even be a member of your church. But have you ever asked Christ to come into your life and committed yourself without reserve to Him? My prayer is that you will do so today.
Then pray for your fiancé and ask God to bring him to Christ also. Life's greatest joy comes from walking with Christ and that joy is multiplied when a husband and wife walk together with Him. May this be your experience as you open your hearts to Him.