As Christians are dhimmis, they (as well as Jews) were tolerated to continue living among Muslims if they pay a tax per person. Mozarabs had their own tribunals and authorities. Some of them had high offices in Muslim courts. Conversion to Islam was encouraged. Conversions to Christianism or Judaism were forbidden. As the Reconquista advanced, they integrated into the Christian kingdoms. They also migrated North in times of persecution.
Language
During the early stages of Romance languages development in Iberia, a set of romance dialects was spoken in Muslim areas of the Peninsula by the general population. This is known as the Mozarabic language, though never was a common standard.
This variety of Romance is the first documented in writing in the Peninsula as choruses (kharjas) in Arabic lyrics called muwashakhas. As they were written in Arabic alphabet, the vowels had to be reconstructed. In some aspects, it is more archaic than the other Romances.
This Romance variety had a significant impact in the formation of Portuguese, Spanish and Catalan (especially the Valencian variety), which explains why these languages have so many words of Arabic origin (Mozarabic was, understandably, quite influenced by Arabic and vice versa).
The cultural language of Mozarabs continued to be Latin, but as time passed, young Mozarabs studied and even excelled at Arabic.
See also aljamiado.
Religion
The Mozarabs remained out of the influence of French monks and conserved the Visigothic rite of Mass, also known as the Mozarabic rite. The Christian kingdoms of the North, though, have changed to the Latin rite (Castile in 1080) and appointed Northern bishops for the conquered sees. Nowadays, the Mozarabic rite is allowed by a Papal privilege at one chapel of the Toledo Cathedral.
The St. Isidro hermit in Madrid also holds occasional Mozarabic masses.
Conversion to Islam opened new social horizons to Mozarabs (not to mention they saved the dhim tax). Some Christian authorities were scandalized at how the young ones preferred the Arabic culture and language and tried to raise confrontation by publicly offending Islam. They expected that, by becoming martyrs, they would visibilize the conflict. The Islamic authorities, though, chose to consider them as madmen, thus deflecting tensions.
See also Elipandus.