consider this line of scripture instead of thinking in absolutes. "Evil men have crept in among you trying to replace the grace of God with a license for immorality"
Grace means you won't face destruction for sinning, God can forgive you. But does that mean you should intentionally go on sinning as if Grace was a license for you to sin? Apparently not.
I'm not a christian, i'll not be a christian and i have no intention to become a christian.
For me, your use of second person pronouns in your sentence give me a feeling you're preaching. It would be much better if instead you use a third person pronouns which to me you'll less look like preaching.
I'm trying to figure out what is the meaning for your statement 'God doesn't say a non-believer (who also is a non-follower) have to quit sinning to be saved', in relation to what you further say 'if a person believe in Jesus he would do what Jesus says, Jesus says a believer (who is also a follower) have to quit sinning'.
Now i think about it, it may means non-believer (who also is a non-follower) don't have to quit sinning to be saved. To be saved, they need to believe in Jesus. If they believe in Jesus then they'll automatically do what Jesus says which is to quit sinning.
So, 'quit sinning' is not a condition for a non-believer (who also is a non-follower) to be saved. Once they believe in Jesus they'll automatically quit sinning.
Maybe it make much sence with my expalnation about your statements, i'll have to think about it.