Catholics, Baptists, Born-Agains, Seventh-Day Adventists and Lutherans all accept each other as Christians. Does that mean that a Baptist is also accepted as a Born again, an adventist, a catholic and a Lutheran?

Ryan, I think that you don't know the correct term for "Christian". 
 
Christian is a term that branches out in many directions- in many different, more specific faiths. Chances are, you're not just "Christian." You're probably Baptist or Catholic or something of the like. 
 
So, I'm Christian. If I accept Baptists as Christian, will they accept me as Baptist?

Christian is not a denomination but a faith in Jesus Christ.  
 
Catholic, Baptist, Protestant, Pentecostal, Mormon, Jehovah Witness' are all denominations of Christianity.  
 
So you being a Christian means you believe in Christ. Just like Mormons believe in Christ, so we are both Mormons! 
 
But unless you believe in the doctrine of our Church you are not Mormon though just like I am not Baptist or Catholic