While Montgomery County Democratic leaders were telephoning each other yesterday in unusual warm displays of postprimary handshaking, Republicans were busy putting up their signs: "Had Enough on Taxes? Vote Republican."

Yesterday, just hours after slates of Democratic and Republican candidates for county executive and County Council were nominated in some hard-fought races, the general election campaigns had already begun.

There is more than enough reason for both sides to get off to head starts in the seven-week campaign because, on the big issue of "dollars and cents" they both concede that there is litttle difference between the Republicans and the Democrats.

Ordinarily, the Republicans, the party of tight pursestrings, should be the beneficiary of the apparent sentiment of taxpayer revolt in the country.

But the Democrats, whose party has 2 1/2 times the number of registered voters in the county as the, GOP are trying to take the issue away from the Republicans.

"Suddenly we have all these born-again fiscal conservatives," said Joseph Kernay, the Republican Party chairman. "Is the voter going to believe a belated convert or one who was pushing this issue even when it wasn't popular?"

In winning 48 percent of the Democratic vote against two opponents. State Sen. Charles W. Gilchrist has put Democrats in an "excellent position" to take over the county executive office for the first time, according to party officials.

That theory is based on Gilchrist's success in winning nearly every prenered personality, which made him the candidate least likely to-rekindle the internal squabbles that have sometimes led dissident Democratic factions to work against their party's nominees.

"The main issue," said Gilchrist, a tax lawyer, "is going to be who can get the growth of expensive government under control and still keep services the public wants."

His opponent, Republican Richmond Gilchrist, who received 48 percent of the vote, beat Planning Board Chairman Royce Hanson, who got 33 percent, and County Council member John Menke, who got 19 percent. Keeney won 57 percent of the Republican vote against 28 percent for Albert Ceccone and 15 percent for Gerald Warren.

M. Keeney, an insurance executive, planning commissioner and former County Council member pointed to his own seven years of local government experience as his chief qualification.

The results of the County Council races were less decisive, but they did result in the narrow upset of one-term incumbent Jane Anne Moore by Michael Gudis, a financial management consultant. When the absentee ballots were counted late yesterday, Gudis held a 325-vote unofficial lead over Moore, who had been dropped from the slate of party regulars.

Gudis will face Republican Barrie Ciliberti, a longtime party worker and Bowie State College teacher. In other council races Scott Fosler, a former county executive candidate, and Rose Crenca, a civic activist and secretary of the Taxpayers' League, defeated four at-large Democrats.

They will face Republicans Malcolm Lawrence, a "back-to-the-basics" school activist, and Taft Holland, a former government analyst.

Incumbent Esther Gelman and Neal Potter won hadily over challengers Alvin Schneyer, a tenant activist, and Helen Strang, a civic activist. Gelman will face Republican Richard L. Bogley, whom she defeated with 61 percent of the vote in 1974. Potter, an economist, will meet Jackie Simon, a Republican with strong business support.

Incumbent Elizabeth Scull. the council president who had no primary race, will face Barbara Bailey; Republican Bob Brennan, a former planning board chairman and builder, will meet Democrat Ruth Spector, a legislative aide to Gilchrist. Neither had primary races.

In the nonpartisan race for the school board, recurring dissatisfaction with Superintendent Charles Bernardo again will dominate the contest. Incumbent Elizabeth Spencer, who earlier this year opposed Bernardo's rehiring, led a field of eight nominees. Two other outspoken Bernardo critics, Joseph Barse and Eleanor Zappone, also were nominated.

Others nominated to compete for four school board slots in November are Frederica F. Hodges, Carol F. Wallace, Sandra M. King-Shaw, Nancy H. Wiecking and Barry M. Kiein.