If you see people who melodiously recite the Quran in public yet behave sinfully in their private lives, don’t be shocked. Sin is a common denominator in all fallible children of Adam. The only difference is that we are all different in the frequency of our sins and the type of sins that each of us engages in.
Secondly, don’t allow this to be a reason to rethink faith altogether. Instead, this should be a reason for your faith to be strengthened. The fact that someone sinful like yourself and myself has also been given the ability to recite the Quran, despite his/her sin, should encourage you to also recite the Quran! The Quran embraces everyone; the sinful, the pious, the young, the old, the Muslim, the non-Muslim, the rich, the poor, and all other types of people.
Moreover, among the signs of the final day is that there will be reciters of the Quran who don’t act by its teachings. If anything, the existence of such people, who are able to beautifully recite the Quran yet fail to act by its teachings, should strengthen your faith as this phenomenon, although evil in and of itself, fulfills this prophecy.
Lastly, if you are that reciter who doesn’t act by the very Quran that s/he melodiously recites, then remember that the Prophet ﷺ said, ❝The Quran can either be a witness for you or against you!❞ [Ṣaḥīḥ Muslim] And remember that Allah said about such people in the previous nations, ❝The example of those who were entrusted to bear the Torah but failed to do so, is that of a donkey carrying books. How evil is the example of those who reject Allah’s verses, and Allah does not guide the wrongdoers.❞ [62:5]