You don't have to do anything means that salvation is free, it cannot be earned. Baptism and repentance are signs of salvation (repentence being critically important), but they do not preceed salvation nor do they qualify one for it (see Ro 3:22-24 NIV).
And If you don't repent, you can't be saved. There is no way around it. You can't be saved and then not repent (Luke 13:3- unless you repent, you will all likewise perish).
It's silly to say someone is saved who has not repented or that repentance is just a sign of salvation. It is a choice a person makes. You can choose to be sorry and change your life, or you can choose to keep living in sin and guilt. It is something you do.
Every verse doesn't tell everything that must be done to be saved. You can't just use one verse and say that's how you are saved. The inspired writers were speaking to different crowds with different situations. Use the Bible in its entirety to see the acts involved in salvation:
Hearing is involved (Romans 10:17-Faith comes by hearing),
Believing is involved (John 3:16, John 8:24),
Repenting is involved (Luke 13:3- unless you repent, you will all likewise perish, Acts 17:30),
Confession of Christ (Rom 10:9-10- confession made unto salvation)
Baptism is involved (Acts 2:38, 1 Peter 3:21, Mark 16:16- he that believeth and is baptized shall be saved)
Remaining faithful unto death is involved (Rev 2:10)
People just take one verse and say we don't have to do anything to be saved. That's what they want you to believe. People try sooo hard to get around these things. It's not about boasting and saying "look at me, look what I did to save myself". It's about fully submitting yourself to God and DOING what he tells you to do if you want your salvation.
God wants us to obey (John 14:15). He never said, if you believe in me but don't want to obey anything I have told you to, it's ok, you can be saved. Show me that in the scripture because that is what you are teaching.