All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
A dissolute person [Faasiq] is the one who commits a great major sin or repeatedly commits minor sins. So if a Muslim commits one of the great major sins like adultery, or fornication, or stealing, or consuming Ribaa (interest or usury) and the like, then he is a dissolute person. Similarly, if he commits a minor sin but insists on committing it again and again and does not repent, he is also considered a dissolute person.
Some jurists consider that credibility is one of the conditions for a person to call the Athaan (call to the prayer) and that the call of a dissolute person is not accepted.
Ibn Qudaamah said: 'The Athaan by a boy or a dissolute person is not counted [accepted and permitted] because Athaan is legislated to inform people, but since their testimony is not accepted then the purpose of informing people is not achieved.' This is the view of the Hanbali school and others and it is also the view of Shaykh Al-Islam Ibn Taymiyyah as he said: 'There are two opinions about whether or not the Athaan given by a dissolute person is permissible, the strongest view is that it is not permissible as he contradicts the commandment of the Prophet . As regards appointing such a person as a Mu'athin (a person who calls to the prayer) then he should not be appointed and there is no difference of opinion on this at all.'
There is no doubt that shaving the beard is forbidden as this is contradicting the command of the Prophet which is to keep it and not to imitate the non-Muslims by shaving it. Please refer to Fatwa: 84474 on this regard.
Insisting on this sin (shaving the beard) is an act of dissoluteness that spoils the credibility of the person, this implies that the Athaan of a person who shaves the beard is not sufficient [not valid] according to the scholars who set credibility as a condition for the person who calls for the prayer. However, some scholars are of the view that it is disliked for a dissolute person to call for the prayer, but if he does so, it is sufficient. Nonetheless, the most correct opinion is the first one.
Allaah knows best.