Certain nouns can often be used as noun adjuncts in place of a corresponding adjective, with no change in literal meaning, where:

• The noun is not pejorative when used nominatively by itself.
• Nor is the corresponding adjective pejorative.
• But the noun used attributively is pejorative.

Is this a common pattern in English (besides the 2 examples below), and if so, what's the reason behind it? Also, is the phenomenon specific to proper nouns?

Examples

Here are some examples of such usages that should be typical according to what I'm claiming:

Jew

Generally not pejorative when used nominatively (though that may depend on the company you keep...):

Who is a Jew?

Corresponding adjective is not pejorative:

The Haggadah (Hebrew: הַגָּדָה‎, "telling") is a Jewish text that sets forth the order of the Passover Seder.

But an anti-Semitic slur when used attributively:

I shoulda known they'd stick me in a room with a Jew cop.

Democrat (the US political party)

Not pejorative, used nominatively:

President Barack Obama is a Democrat.

Not pejorative, corresponding adjective:

The Democratic Party is one of two major contemporary political parties in the United States[.]

Pejorative, used attributively:

Democrat Party

DEMOCRAT POLITICIANS' LUST FOR TAX MONEY OUTWEIGHS THEIR SUPPOSED COMMITMENT TO SOCIAL JUSTICE

I feel the "reason" behind it is simply that to use a noun adjunct is to equate both nouns, and therefore emphasising the former adjective to the same semantic level as the noun itself. Using an adjective and a noun is normal, and the noun is nominal; and the adjective normally modifies the noun. But a noun adjunct equates the two together, so that the so-called "Jew Cop" is both a cop and a Jew. But one could imagine a situation where surprise would account for the same use.

One probably finds these constructions more common in impassioned speech, both negative and positive, as Mechanical Snail mentioned. Therefore I disagree with your premise that this construction implies a pejorative sense, but it is, rather, an emphatic sense.

I can think of at least one example of the pejorative noun modifier: A "female driver" is simply a member of a demographic group, with no good or bad connotation. A "woman driver," however, is almost certainly using the rear-view mirror to put on her lipstick.