A single word for labelling someone a disbeliever in a particular religion despite them adhering to it

Solution 1:

If I understand the question correctly I would use the word "nominal" e.g. a nominal christian. From http://dictionary.reference.com/browse/nominal 1.being such in name only

Solution 2:

I think the best word would be heretic. A heretic claims to be a believer, but either professes ideas contrary to the official religious doctrine or rejects ideas included in that doctrine.

During the Reformation (and in some contemporary circles, for that matter) a Catholic would have called a Protestant a 'heretic', though the Protestant would have called him/herself a Christian.

The judgment is ultimately subjective.

Solution 3:

Though hypocrite is the probable expected one-word answer, there is another concept which fits the description. Throughout history there have been many instances where an invading or ruling class forces a group of people to convert to the main religion (at least in the west this has occurred in many directions among Christians, Jews, and Muslims). In English such a person is called a:

forced convert

Many convert altogether, but some, despite outwardly keeping the converted practices, maintain hidden privately the religious practices and beliefs of preconversion religion (and this can be for generations).

There are a number of specific terms for a Jew who was forced to convert but maintained practices and/or beliefs in private (and descendants who maintain them too). The accepted term in English is the borrowing from Hebrew:

anusim

which means 'coerced'.

Solution 4:

I think the normal word is 'hypocrite'.