Can anybody provide a single word for labelling someone a disbeliever in a particular religion despite them adhering to that religion?
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
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.
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:
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:
I don't know about other belief systems, but Christians commonly refer to this as in name -- as in somebody is a Christian in name if they label themselves as Christians but don't actually believe in its tenants or live by them. It is also common to use expressions like cultural Christian for those who let themselves wear the label but don't actually know or believe in the teachings.
In spite of the dictionary definition being so similar, the term nominal tends to have a different shade of meaning than saying in name. A nominal Christian, for example, would imply a shade stronger adherence to the beliefs, but would be somebody who doesn't take them very seriously.
If the disbelief you mention is more active than passive, you could call them doubters or dissenters. It's possible to belief something and yet doubt aspects of it, in which case it's acceptable to be labeled like this. However at some point, if the doubting or dissenting becomes the defining feature, stronger descriptors such as hypocrite start becoming appropriate. Somebody who actively disbelieves rather than just questions and yet still labels themselves as Christian eventually stops having the right to use that label at all. If you keep down this path of holding dissenting views and yet claiming those views belong to the whole, eventually you become a heretic. Note that it's somebody who does not claim that their beliefs are Christian at all can't be labeled as a heretic. Heretical teachings give false doctrines under a wrong label.
It defines Judaism as the cultural and historical experience of the Jewish people and encourages humanistic and secular Jews to celebrate their Jewish identity by participating in Jewish holidays and life cycle events (such as weddings and bar and bat mitzvah) with inspirational ceremonies that draw upon but go beyond traditional literature.
It would fit a specific type of disbeliever - so it might be completely inappropriate. Also, it seems to be a common term only for Judaism.
You should define what kind of adhering and for what purpose is going on for the term you seek.
Is it possible to adhere to a religion and not believe it? Usually belief is one of the requirements of most religions.
Anyway: I'm a Christian and when my Christian friends don't go to church I say they're a "heathen" or a "backslider"
Or for add emphasis you could say a "heathen backslider"
You could also say "non-practicing" as in "I'm a non-practicing Catholic"