To hear his aides tell it, Virginia's Independent Sen. Harry F. Byrd Jr. is merely going to a friend's picnic today and joining other state officials in welcoming President Reagan at a fund-raising dinner in Richmond on Thursday.

That both appearances will be made with Republican gubernatorial candidate J. Marshall Coleman is, they say, without political significance. Byrd is a staunch Reagan supporter, they say, and has frequently attended the fall picnic at the home of Lawrence Lewis.

But Virginia Republicans, who last week put new pressure on Byrd to switch to the Republican Party or face a challenger in 1982, are not so easily convinced that his scheduled appearances are meaningless.

"Anybody who buys that is extremely naive," said LaRonda Hudgins, a Coleman campaign chairman in Hampton. "You have to see his presence as significant assistance to the Coleman campaign."

If nothing else, Byrd's attendance at two GOP functions in one week may suggest some shift in the senior senator's traditionally neutral stand in state elections. "If he'd wanted to play it straight down the middle, he probably would have stayed away," said one GOP official, who asked not to be named.

Virginia Republicans also are watching for signals from Byrd because they carry implications for whether the party will nominate a candidate to challenge him in 1982.

Republicans have asked Byrd, scion of the state's most famous political family, to join their ranks since 1976. In that election, Byrd, who had left the ruling Democratic Party six years before, declined but still received tacit Republican support.

Given Byrd's consistently conservative votes and clout in the Senate and his support from state conservatives, it was an arrangement that most Virginia's Republicans, some of them former Byrd Democrats, could live with.

But now, said GOP Chairman Alfred B. Cramer III, "The climate has changed. We have proven again and again that Republicans can win in Virginia as Republicans."

In spite of the pressure and in keeping with his low-key style, Byrd has stayed mum on his intentions in 1982. He could run as an Independent and continue sitting with the Democrats in the Senate. He could maintain his independence but switch to the Republican side of the aisle. He could convert to the GOP or he could retire.

"He hasn't made up his mind," Byrd press aide Will Marshall said.

But if Byrd is acting coy, the Republican Party is getting impatient. This week, Cramer warned the senator anew that unless he makes some move to join the GOP, he will certainly be opposed by a Republican in next year's election.

"If the senator decides to run as an Independent and a Democrat, the Republican Party will consider him a Democrat and he will have opposition," Cramer said. "We've sent him our love and if he spurns us . . . I won't say we would be like a woman scorned, but it would be unrequited love."

If Byrd sticks with the Senate Democrats, or if he retires, the most likely Republican contender is Rep. Paul S. Trible Jr., who has repeatedly said he would be "interested" in running if Byrd retires.

A spokesman for Trible said last week the congressman is not ready to make a commitment to a 1982 Senate race. But most Republicans predict that Trible would certainly be the nominee to run against an Independent/Democrat Byrd, and possibly even against an Independent/Republican Byrd.

"It's a very delicate situation," said John Alderson, vice chairman of the party and former chairman of Reagan's Virginia campaign. "If Byrd ran as an Independent and caucused with the Republicans, that would satisfy me but it would still not ensure that the party will not present its own nominee."

Given that scenario, the Republican leadership might be unable to stop a nominating stampede at next summer's state GOP convention, Alderson said. "It's an entirely different thing to muster people to a convention not to nominate a candidate," he said.

"A party exists to seek qualified candidates for office," Cramer said. "If we do not do that, we will have abrogated our responsibility."

Other Republicans, backed by national party officials, are pushing for Byrd to switch for the good of the GOP. "The mood is that he should at the minimum join the caucus," Hudgins said. "Ronald Reagan needs all the support he can get."

If Byrd does become a Republican, party officials are hoping he will do so before this November's election so he could lend open support to the GOP ticket. "We'd like to see him announce right now and sit in the Republican caucus right now," Cramer said.

But so far, Byrd is keeping his own counsel. As for Republicans, the message implied by his attendance with Coleman at Lewis' picnic and at the Richmond fund-raiser is welcome, but it's not enough.

"We are heartened by the fact that he is attending," GOP spokesman Neil Cotiaux said. "And as far as Virginians infer that he is disposed to look favorably on our ticket this year, we are certainly pleased."