SBC is less conservative than Independent Baptists, most of whom still use the hymns that SBC has spurned for two decades now. If an SBC church preaches The Bible, it is fine; non-denominational would be acceptable too if the church is Bible-based.
I would like to see a hymnal used by Independent Baptists. The United Methodist Church, which I belong to, spurns scores of great hymns, including dozens composed by prominent Methodists, that were once widely sung. Even "Eternal Father, Strong to Save," a staple in most Protestant hymnals, cannot be found in the United Methodist hymnal.
I'm preacher's kid, raised on old hymns, and I love them. But, my preference of hymns over newer worship music is my opinion, not a God inspired, Bible based doctrine.