Question: "Should Christians of different denominations date or marry?"
Answer: Can a Baptist date a Pentecostal? Can a Lutheran date a Presbyterian? The most important issue is whether both individuals know Jesus Christ as Savior. The Bible speaks of being "unequally yoked" (2 Corinthians 6:14), but this only refers to believers and unbelievers. It does not refer to two believers who happen to have some beliefs that are different. If both individuals know Jesus Christ as Savior, there is no reason, biblically, that they could not date and/or marry.
However, that is not to say there will not be potential problems and issues. When / if the relationship becomes serious and is potentially leading toward marriage, the couple must sit down and come to an agreement on what church to attend. If there are major disagreements in doctrinal beliefs, the couple must agree to disagree, and at the same time agree on how to raise children and agree on how to live out the Christian faith. It is best for a couple of agree doctrinally, but the most important issue is faith in Christ, love for one another, and a desire to have a God-honoring relationship.
That said, it goes without saying that this applies only to different denominations of the Christian faith. True believers in Christ should not marry members of cults and/or false religions that claim to be Christian. Knowing and agreeing on the basic doctrines of the Christian faith is crucial for a couple who hope to have a successful, God-honoring relationship or marriage.