“A proper noun is a noun that in its primary application refers to a unique entity, such as London, Jupiter, Sarah, or Microsoft, as distinguished from a common noun, which usually refers to a class of entities (city, planet, person, corporation), or non-unique instances of a certain class (a city, another planet, these persons, our corporation).Some proper nouns occur in plural form (optionally or exclusively), and then they refer to groups of entities considered as unique (the Hendersons, the Everglades, the Azores, the Pleiades). Proper nouns can also occur in secondary applications, for example modifying nouns (the Mozart experience; his Azores adventure), or in the role of common nouns (he’s no Pavarotti; a few would-be Napoleons). The detailed definition of the term is problematic and to an extent governed by convention.”

So while there is some subjectivity to this…

Unless the group of christians in question is a specific group – for instance if you were reporting on a softball game between a specific church and mosque, and wrote “The Christians got stomped by the Muslims.” – people being referred to by their religious affiliation is not a proper noun. The only way they would be, is if a general word existed that we used more often – like deist – and then we used words like scientologist or hindu to specify what kind of deist we’re talking about in this example. Those would only be proper nouns, if religious people were treated as a general entity, and christians a unique version of them – they aren’t. Though one could argue, in that case, that christian isn’t a proper noun, but Catholic is, because it’s a specific and unique subset of christians.

And for that matter, officially, the words texan or american are also NOT proper nouns. By convention, they are made capital based on their base word – i.e. Texas or America – being a proper noun. But while some writing style guides do direct you to capitalize the words, they do not qualify them as proper nouns – the directions are based on convention and nothing more.

And the same applies to capitalizing Christian and Sikh. By convention, people have capitalized them, because Christianity and Sikhism are capitalized. But they are just nouns – or in the case of “He’s a christian pastor,” they are adjectives. And as such, unless you are following a specific style guide, there is no reason to capitalize them.

He is a christian monk.

He is of christian belief.

His name is Christian.