How can a Christian reject part of the Bible and still call themselves a Christian?

[Lek]

And to clarify further, I'm specifically referring to denominations that reject Christ's teaching forbidding remarriage following divorce, and Christ teaching that practice is actually adultery and clearly, is forbidden in the 10 Commandments, and that they allow such remarriages in their facilities, and provide approved pastors to consecrate such marriages.  And such couples are then allowed to worship in regular services at those churches without repudiating their continuing adulterous relationship.

You're right on this one. That's a problem with religions. A human institution takes the place of following Christ.