Saying one is a Biblicist is not clear because all the denominations are going to say that.
The divisions of 1 Corinthians was a division within the local church in general. The problem was not so much people 'preferred' other teachers, but that those teachers were being pit up against Apostolic leadership, specifically Paul. Notice Paul said it was equally as bad to say "I'm of Christ" not because we shouldn't be of Christ, but because that was being used as another way to say "See, I'm better then you followers of Paul because I'm a follower of Christ" arrogantly.
I'm not here referring to your particular faith journey, though we all have fallen in the pit and will go back into the pit without Christ.
I'm speaking of our doctrinal understandings that under gird our faith; teaching is incredibly important. If you believe in the Sacraments, I'm going to approach discussions with you differently than if you say 'Lord's supper is just a memorial service, there is no specific grace imparted by observing it.' This is just one of many questions.
When we say we don't take a stand on any particular issue or denomination or a church, we're opening ourselves up to 'eclectic' religion, which I believe is **very** dangerous. In 'eclectic' religion, we simply accept what everyone's telling us. We have no real anchor in any real church; we have become an island unto ourself and we pat ourselves on the back saying "I follow Christ and the Bible and to heck with denominational churches". We do ourself a dis-service because if the basics of Christianity is true (we are all sinners without Christ), how can we trust our own ideas and interpretations? How can we know we're not deceiving ourselves or making an idol of God by own own fanciful scriptural interpretations?
Well, we have the Holy Spirit ... and the Holy Spirit is spoken of as being intimate with God's churches (again 1 Cor 12). He is the one to guide us into all truth.
Now, I'm not suggesting don't think for yourself; I'm not suggesting go join a group like Bruderhof (as alluring as it may seem). I 'm not saying allow yourself to be abused by pastors or people.
But I am saying that without a church, you wind up trusting yourself and hoping that what you believe is the truth. You can't bounce that idea off of someone else and, worse, you can't help others propagate the same truth you've discovered to the world.
Basics: salvation is by faith alone in Christ alone and His redeeming work alone. From here, we should pray what church God wants us in because He is using each denomination that believes solely in the Bible and Christ to His glory. In my scenario, I am not limiting God by insisting believers join local churches. I am expanding by suggesting God will lead us to the right denomination. I do not consider orthodox denominations to be 'factions' of Christ when everyone realizes - hey, we're trying the best we can going along with the Scriptures and staying true to our personal beliefs. We may have differences; that's okay. We may not necessarily all get along, but we can disagree amicably.