Tanzania has not asked a religion question in its national census since 1967. The omission was deliberate policy under Julius Nyerere, whose project was to build a nation on Swahili language and ujamaa rather than on ethnicity or faith, and who judged that publishing an authoritative religious head count in a country this evenly divided would turn every subsequent political question into a confessional one.
The result is that nobody knows the ratio. Estimates from surveys and from religious bodies themselves differ, and both Christian and Muslim organisations have at times claimed a majority. That uncertainty is itself politically useful to everyone and politically dangerous to everyone, which is roughly the equilibrium Nyerere intended.
The live constitutional argument is about kadhi courts. Zanzibar, which retains its own legal system under the union, has kadhi courts applying Islamic personal law in matters of marriage, divorce and inheritance for Muslims. The mainland does not; such courts were abolished shortly after independence, and Muslim personal law matters are handled in the ordinary courts. Muslim organisations on the mainland have pressed for their reinstatement for decades, arguing that the present arrangement leaves Muslims worse served than they were under colonial rule. Christian bodies have opposed it, arguing that a religious court system in a secular state creates parallel law and that the pressure would not stop at personal status.
Successive governments have promised and then dropped legislation, and the question has been one of the recurring obstacles in the long stalled process of writing a new constitution.