I’d suspect you wouldn’t find a correlation because contraceptive access is probably similar across the board in many low income countries. While they probably have the higher fertility rate overall still, access to something says nothing about uptake. In addition years of HIV advocacy by NGOs has pushed condoms as a means of HIV prevention as well, so there are health reasons why people would use condoms that wouldn’t conflict with their religious beliefs — if there is one in these countries that’s preventing contraceptive use. So to even get the contraceptive access data you have to define what access even looks like.

You’d probably find more of a pattern mapping average incomes or rural vs urban or the education of the mothers (this almost always tightly correlated).

I don’t even trust this data since there’s no way these are accurate reports of country wide worship attendance.