"Yellow Dog Republican" is redundant. The fact is, Republicans hardly ever cross party lines; rather, as a statistical matter, Republicans virtually always vote for Republicans.
Democrats, on the other hand, have a much lower degree of party loyalty, and frequently cross party lines. For example, Democrats will frequently vote for progressive Republican candidates in the northeast and the west; and, the so-called (conservative) Reagan Democrats will often cross party lines, John McCain being a case in point.
The reason is simple. The Democratic party is far more diverse than the Republican party and, to be blunt, more open minded. Republicans, however, are of three general types: (1) people worried about their money (most typically, the "county clubbers" and wannabe country clubbers); (2) social conservatives (most prominently religious reactionaries); and (3) those with an anti-government/libertarian bent. Virtually all Republicans -- excepting the odd racist and/or xenophobe -- fall into one of these three categories; and, these folks either vote Republican or do not vote at all.
Hence, it would be superfluous to use the phrase "yellow dog Republican" -- all Republicans are yellow dog Republicans, while only a small subset of Democrats will always vote for a Democrat.