Medieval polemic had Muslims convert from Islam to escape austerity

Evidence

Indeed, they believed that it was meritorious to provoke filthy appetites. Muslims who were not taken up with the pleasures of the flesh sought baptism. Thus it was that especially in the hot regions of the East ‘rough and lustful’ men found the straight way and narrow gate intolerable; instead it was the fatal wide and broad way which they chose to follow. — Norman Daniel, Islam and the West, 857