Rep. John J. Rhodes (R-Ariz.), who for 30 years has been a moderate voice and a mediator in Congress, is keeping himself aloof from Tuesday's Arizona Republican primary, a scramble among a field of four, a woman and three men known as "Donna and the Monotones," who aspire to be his successor.

Whoever wins the Republican nomination in Rhodes' home district is virtually assured of election in November. Registered Republicans outnumber Democrats 51.4 percent to 39.9 percent.

Rhodes, who is retiring at the end of his 15th term, and who has stepped aside as House minority leader, has declined to endorse any of the GOP candidates. The closest Rhodes came to making an endorsement was when his son, Jay, gave some thought to running for his father's seat before deciding against it.

In both the gubernatorial and Senate primaries, polls show moderate Republican candidates leading more ideological rivals by nearly 2 to 1. The winners will challenge the Democratic incumbents, Sen. Dennis DeConcini and Gov. Bruce Babbitt.

Contestants in the GOP congressional primary are John McCain III, a retired Navy officer and former prisoner of war in North Vietnam; state Rep. Donna Carlson-West of Mesa, Rhodes' home town; state Sen. Jim Mack of Tempe, home of Arizona State University, and Dr. Ray Russell, a Mesa veterinarian.

The fact that they all are fiscal conservatives who admire President Reagan and often sing the same political tune inspired their derisive nickname.

McCain, 46, who was held in Hanoi for six years after his plane was shot down, suffers the label of carpetbagger. He settled in Arizona just 18 months ago, but says the longest he lived anywhere was the time he spent in captivity in Hanoi. His father and grandfather were admirals.

McCain also has been criticized by local Mormons because he is a vice president for the main Budweiser distributor here. He married the boss' daughter.

Despite those attacks, the polls show McCain 6 percentage points ahead of his nearest rival, Russell, with more than one-third of the voters undecided two weeks before the election. He has spent more than $300,000, nearly equal the total of the three other candidates.

This is McCain's first run for public office, but he has high-powered supporters. Sen. John G. Tower (R-Tex.), chairman of the Armed Services Committee, campaigned here for McCain Wednesday. Tower remembers McCain from the four years McCain served as Navy liaison in the Senate.

Carlson-West, 44, who has served four two-year terms in the Arizona House of Representatives and was a state senate staff member for more than seven years before that, was the front-runner early in the campaign. But contributions declined, and so did her support.

She is a strong opponent of the Equal Rights Amendment and is a right-to-life advocate. When McCain was criticized for accepting contributions from his beer company employer, she said she regularly returns donations from Arizona liquor interests. Later, however, she admitted that she had accepted contributions from the Coors family.

Mack, 48, has 12 unspectacular years in the state senate to his credit. He boasts in television ads that he is the president pro tem of the senate, which means he presides when the president is absent.

Russell, 50, is making his first political race. He has been president of 24 organizations, including a local Boy Scout unit and the Mesa Chamber of Commerce, and is active in the Mormon church.

Most experts agree the race is a tossup, with none of the candidates completely out of the picture.

In the Senate contest state Rep. Pete Dunn of Phoenix has a big lead over Mesa real estate investor Dean Sellers, who is supported by New Right activists. State senate president Leo Corbet is favored over former state senator Evan Mecham, a conservative and combative candidate who has lost two previous gubernatorial primary campaigns, in 1964 and 1972, and a U.S. Senate race in 1962.

The winner's task against the politically strong Babbitt will be complicated by the presence on the Libertarian line of former representative Sam Steiger, who will draw off Republican votes.

Rep. Morris K. Udall (D-Ariz.) has no primary opposition, and because his newly drawn district is nearly two-thirds' Democratic, is expected to have no trouble winning the general election.