This could happen, of course, and not just if we become so used to a particular style of worship that we forget its meaning. Jesus warned us against "vain repetitions" when we pray that have no real meaning (Matthew 6:7, KJV).
But this could happen whenever we worship, if we allow our minds to wander. Sit down someday and quietly read through the words your church uses every week; I suspect you will find they have great meaning. You also will find that they are based on the Bible–and that their central theme is Christ and what He has done for us. And after all, this is the foundation for all true worship, "For no one can lay any foundation other than the one already laid, which is Jesus Christ" (1 Corinthians 3:11).
Churches differ in the ways they worship (as you are discovering)–but whenever the focus is on God and what He has done for us through His Son, these differences will begin to fade. The key is our hearts, and whether or not they are attuned to God. Jesus said, "God is spirit, and his worshipers must worship in spirit and in truth" (John 4:24).
Ask God to keep your heart and mind focused on Him whenever you worship–not only each week in your church, but every day as you spend time alone with Him in His Word and in prayer.