Three Dallas County judges today ignored an appeal by Democratic Gov. Mark White and declared themselves Republicans, adding to Democrats' postelection blues in this emerging two-party state.

Accompanied by Sen. Phil Gramm (R-Tex.), who undertook a similar transformation two years ago, State District Judges Thomas Thorpe and Don Koons and County Judge Mike Schwille announced that the Democratic Party has become "too liberal."

All face reelection in 1986.

"I guarantee you, you're going to see more switches before too long," said George Strake, chairman of the state Republican Party, which has been courting conservative Democratic officeholders since President Reagan's landslide reelection swept record numbers of Republicans into county offices and the state legislature.

Strake said he expects that a dozen county officials will change parties within a few months and that at least two state legislators will switch after the session adjourns this spring.

"The Democrats have been making our job a lot easier for us," Strake said. "Mondale, Ferraro, [Lloyd] Doggett [the state senator defeated by Gramm in November] and now Paul Kirk -- it's just one more position in the Democratic Party going to a liberal who is anathema to most Texans."

State Democratic Chairman Bob Slagle apparently concurs.

Exercised by the recent election of Kirk as Democratic National Committee chairman, Slagle said last week, "We don't need their DNC's help, and we don't need their interference and we don't need them slopping things over on us." He said he doubted that Texas Democrats would see the election of Kirk, a former chief of staff for Sen. Edward M. Kennedy (D-Mass.), as "a moderate signal."

Slagle made it clear today, however, that he does not think Kirk's election prompted the judges' party-switching. "Let's face it," he said, "Texas has become a bona fide two-party state."

In much of the South, Republicans have been bedeviled by an inability to translate popularity in presidential elections into grass-roots victories. But the Dallas experience demonstrates how rapidly those roots can be rerooted.

In 1978, no Republicans sat on the Dallas bench. With today's switches, 61 of 68 judges there are Republicans. A similar transition has taken place in Harris County (Houston), where two-thirds of 95 sitting judges are Republicans.

Both counties have grown massively in the last decade, largely because of a white-collar influx. Still, Republicans said they believe that they can make grass-roots gains in areas of Texas less affected by Sun Belt demographics.

This spring, a special election is scheduled in rural northeast Texas, where Rep. Sam B. Hall Jr. (D) is giving up his seat to become a federal judge. "I think we've got a shot at winning it," GOP strategist James Francis said. "And you're talking about a district that was represented by Democrat Wright Patman for 50 years."

Republicans have also targeted White in 1986. They think he blundered by calling the three judges to Austin for a loyalty pep talk, if only because he succeeded in giving their defection more media prominence. "He upped the ante with a losing hand," Dallas Republican Party Chairman Fred Meyer said.

White's approval ratings were "higher than a cat's back" through much of last year, Strake said, but have dipped under 45 percent since the November election.

The GOP's strategy, he said, is to run candidates in 1986 against White; Agriculture Commissioner Jim Hightower, who has angered agribusiness interests with a set of pesticide regulations; and Attorney General James Mattox, who goes on trial Monday in state court on a commercial-bribery charge.

A poll last month for a Texas newspaper chain showed that 49 percent of Texas voters identified themselves as Republican or leaning that way, while 42 percent identified themselves as Democrats or leaning that way.