The key is finding the statutory definition of "place of public accommodation, resort, or amusement" which can be found in the definitions section relating to the Louisiana Commission on Human Rights of which "§2247.1. Breastfeeding; discriminatory practices prohibited" is a part. It is:
Section 51:2231 (10) Place of public accommodation, resort, or amusement" means any place, store, or other establishment, either licensed or unlicensed, which supplies goods or services to the general public or which solicits or accepts the patronage or trade of the general public, or which is supported directly or indirectly by government funds. However, a bona fide private club is not a place of public accommodation, resort, or amusement if its policies are determined solely by its members and its facilities or services are available only to its members and their bona fide guests.
Doesn't look to me like a house of worship is encompassed by this definition so this public breastfeeding law does not apply to houses of worship.