Can we have rational and irrational faith?

No. "Rational faith" is a contradiction in terms; it is not possible for any such thing to exist. It is important to distinguish between faith and reasoned conclusions; for example, the premise that the laws of logic apply to the real world (notwithstanding that they are strictly a manmade creation, only intended to mimic the way the world works) is a reasoned conclusion because they work, not an act of faith. Faith is not only unnecessary, it is absolutely evil: it is the deliberate rejection of the ability to apply logic to evidence and reach valid conclusions.