The OP has unintentionally misstated the issue. There's nothing wrong with using the term Democrats to refer to members of the Democratic Party. The issue arises when someone refers to the "Democrat Party" or "Democrat policies" instead of "Democrat
ic Party" and "Democrat
ic policies". "Democrat Party" is not the legal name of the party nor is it proper English. It's used by Republicans as an intentional slur, therefore it can be a sore point among Democrats.
If you unintentionally misuse it and someone corrects you, try not to take it personally. It's simply people fighting Republican's manipulation of language.
See here:
http://mediamatters.org/items/200608160005 In recent months, media figures, including news reporters at CNN, The New York Times, The Wall Street Journal, the Chicago Tribune, and the Associated Press echoed Republicans by employing the word "Democrat" as an adjective to describe things or people of, or relating to, the Democratic Party -- including referring to the "Democrat" Party itself, even though that is not the party's name. The ungrammatical conversion of the noun "Democrat" to an adjective was the brainchild of Republican partisans, presumably an attempt to deny the opposing party the claim to being "democratic" -- or in the words of New Yorker magazine senior editor Hendrik Hertzberg, "to deny the enemy the positive connotations of its chosen appellation." In the early 1990s, apparently due largely to the urging of then-House Speaker Newt Gingrich (R-GA) and Republican pollster Frank Luntz, the use of the word "Democrat" as an adjective became near-universal among Republicans.
Hertzberg pointed out in an article for the August 7 issue of The New Yorker that the word "Democrat" is a noun, arguing that its use as an adjective defies the rules of English grammar:
The American Heritage College Dictionary, for example, defines the noun "Democratic Party" as "One of the two major US political parties, owing its origin to a split in the Democratic-Republican Party under Andrew Jackson in 1828." (It defines "Democrat n" as "A Democratic Party member" and "Democratic adj" as "Of, relating to, or characteristic of the Democratic Party," but gives no definition for -- indeed, makes no mention of -- "Democrat Party n" or "Democrat adj".) Other dictionaries, and reference works generally, appear to be unanimous on these points.
Hertzberg noted that Republicans "as far back as the Harding Administration" have referred to the "Democrat Party," including late Sen. Joseph McCarthy (R-WI), who "made it a regular part of his arsenal of insults," and former Sen. Bob Dole (R-KS), who "denounced 'Democrat wars' ... in his <1976> Vice-Presidential debate with Walter Mondale ."