Isadora goes back to the name Isidore, which also means Isis' gift, however, there was a saint by that name, so I would not consider it at all sacreligious. Isa is also a shortened form of the names Isaac and Isaiah (used both for both genders), as well as Isabel, itself a variation of Elizabeth. Isaac meaning laughter, Isaiah meaning salvation of God; the Lord helps me. So if you would rather look at the name as a combination of either of those names and the name Dora ("gift"), then perhaps you would feel more at ease using it.
Not all of that information was from the BtN database, and may not be exactly reflected there.