Is there a sin of loving a person who is pure Muslim but the other one is converted? Is there a possibility that they can be successful a couple in a future?
There absolutely no difference between a born Muslim and one who converts. What would differentiate individuals is their religious fidelity and allegiance to God. The born Muslim is not pure as there is no religious classism in Islam. If two people choose to be together and they lead a healthy, positive relationship within the guidelines of religion then the success of it is up to them.
I hope this helps.
God knows best.