The American Baptist you mentioned is not the American Baptist Association,Nearly half of Baptist churches in the U.S. are Southern Baptist conservative, evangelical, and focused on the authority of Scripture, It is the largest Protestant denomination in the U.S.
The liberal Baptists are from the American Baptists church who split from the mainline Baptist over theological and social issues.
Reformed churches, are separate from Baptists and emphasize doctrines rooted in Reformed or Calvinistic theology.
The name on the church matters little; to know if it is good, you'll have to visit and discern whether the preacher has the Holy Spirit.
The ABA churches are not liberal, just the opposite.
There is another group in the South none as Baptist Mission Association.
Very little difference in the two.
Some SBC churches are very liberal. Most in the South are not.