How can the statement of the author of "Al-Mughni" and "Al-Rawd al-Murabba'" regarding a disbeliever embracing Islam by performing prayer be reconciled, and do scholars differ on this issue?

The meaning of "Muslim by ruling" for a disbeliever who prays is that he is ruled to be a Muslim based on outward appearances and treated as such, while his inner state is left to Allah. There is no contradiction between the statements of the jurists on this matter, as a disbeliever is ruled to be a Muslim by performing prayer, unless his apostasy was due to denying another obligatory act or slandering a prophet, etc., in which case he is not ruled to be a Muslim merely by prayer. So, whoever disbelieves by denying an obligatory act or the like, his repentance is by affirming what he denied, in addition to the two testimonies of faith.