Is it permissible to pray half an hour after Fajr prayer, or is that considered a departure from the religion?

Among the best acts of worship is prayer (Salah). The Prophet (peace be upon him) prohibited supererogatory prayers (Nafl) at certain times, including after the Fajr prayer until the sun rises. The prohibition here applies to absolute supererogatory prayers that have no specific reason. As for prayers that have a reason, such as Tahiyyat al-Masjid (greeting the mosque), they are performed whenever their reason is present. The statement that praying at this time constitutes apostasy (leaving the fold of Islam) is false, and it is a statement against Allah without knowledge; its utterer must repent. Performing supererogatory prayers at this time is forbidden, and the one who does so exposes himself to sin, but it is not disbelief (kufr).