Galatians 3:26-27 - "For in Christ Jesus you are all sons of God, through faith. For as many of you as were baptized into Christ have put on Christ. There is neither Jew nor Greek, there is neither slave nor free, there is no male and female, for you are all one in Christ Jesus." Paul touches on racism and sexism and maybe if he were writing today in our cultural context, he might include ageism.
With a careful study of both Philippians 2:1-4 and Ephesians 2:14-25 you don't find the apostle's teachings advocating division in the church, or establishing separate worship meetings to suit various styles or different groups of people. Rather sacrifice, tolerance, love, and respect for others are the qualities we are challenged to as the church.
There is no more a place for generational barriers than racism, sexism, or snobbery of any kind. Amazingly you can find snobbery on opposite ends of any given spectrum of worship or music styles. There generally was no hint of a generation gap in the worship of the church found on the mission field in places like we served in Zimbabwe. This idea of independence rather than interdependence is more of a phenomenon of the West and our culture that has tended to affect the church in an unbiblical way.
"I will make Thy name to be remembered in all generations: Therefore shall the people praise Thee for ever and ever." (Psalm 45:17) Making His name known and remembered from generation to generation to generation leads to the result of the people praising Him! From generation to generation, one in Christ will we praise Him! mjm