Is it permitted to rent a storefront from a church?
This is permitted, though it is better to avoid it.
Although it might belong to a church, I understand that the storefront is clearly separate from a place of worship, and therefore there is no prohibition of actually using it (see, for instance, Teshuvos V’hanhugos 2:410; Chai Ha’Levi 4:63).
The problem, however, is that money is going to the church, which is forbidden by the Tosefta (Avodah Zarah 7:1; see Gemara 13a; Gemara 51b and commentaries; Mishneh Le-Melech 7:18; Shulchan Aruch, Yoreh De’ah 143:5; Shulchan Aruch 143:3; Mishnah Berurah 649:4).
However, today the church uses most of its money for a variety of purposes, and therefore there is room for leniency (see Minchas Yitzcahk Vol. 4, no. 88).