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.
It is really sad to hear what you mentioned in the question. Theft leads people to abandon performing the prayers in the mosque due to their fear about their own selves or their money which a grave sin on the part of those who cause this to happen.
We have already issued Fataawa 89476 and 86096 clarifying that theft is forbidden and we mentioned the punishment on a thief in Islam, so please refer to them.
Hence, the rulers should fear Allaah and arrest those thieves and stop them from stealing.
As regards whether or not those thieves are still considered Muslims, the answer is that whoever believes that stealing is permissible, then he is a disbeliever as he denied something which is proven with absolute evidence in Islam, which is that theft is forbidden. Nonetheless, he who steals while knowing that theft is forbidden cannot be considered as a disbeliever even if he is a transgressor or a dissolute person who committed a great major sin because theft does not take the person out of the fold of Islam [does not render him a disbeliever]. This is why the punishment for a thief is to cut his hand whereas the punishment for an apostate is death. However, it is only the Muslim ruler or his deputy by proxy who may enforce these rulings, and not the general public otherwise this could lead to anarchy. In addition to this, when applying the corporal punishments imposed by the Islamic Law, the conditions for applying any rule should be fulfilled while there should be no impediments preventing from implementing such rules. This is something which only the judges could know.
Allaah Knows best.