The endpoint GET Types table values will get any table defined in the system.

Not sure if the ID are different depending on the sites but this is what I see on mine.

2993: Anglican
2994: Baptist
2995: Buddhist
2996: Catholic
2997: Christian
2998: Episcopal
2999: Greek Orthodox
3000: Hindu
3001: Islam
3002: Jewish
3003: Lutheran
3004: Methodist
3005: Non-Denominational
3006: Presbyterian
3007: Protestant

It would be a PUT not a POST since it related directly with the user's general field:

Request URL:  https://<site>.myschoolapp.com/api/user/4125343/?t=${token}

Method: PUT

PUT Params:

{
    "id": "4125343",
    "ReligionTypeId": "3000"
}