Congressional redistricting has given Democratic Rep. William L. Clay, the only black in the Missouri congressional delegation, a district that is whiter, more conservative and much tougher for him to win than any of his previous races.

And, in state Sen. Allan G. Mueller, Clay faces his strongest challenger since he was first elected in 1968. Clay is Missouri's only incumbent congressman facing a tough challenge in today's primary.

Across the state, the retirement of Democratic Rep. Richard Bolling of Kansas City, a 17-term House veteran and chairman of the Rules Committee, has created a wide-open race with eight Democrats and seven Republicans entered in their primaries. In Kansas City, like St. Louis, the Democratic nomination generally assures election in November.

Of the 11 Democrats competing for the chance to oppose Republican U.S. Sen. John C. Danforth on Nov. 2, state Sen. Harriet Woods is considered the clear front-runner. Democratic polls indicate Danforth may be vulnerable because of his strong support for President Reagan's economic program.

Independent polls show Woods with a 3-to-1 lead over her nearest challengers, consumer advocate Tom Ryan and banker and Democratic fund-raiser Burleigh Arnold.

In another primary today, in Kansas, there is a heated three-way Republican race for the gubernatorial nomination to face Democratic Gov. John Carlin, who faces only token opposition for renomination. Wichita multimillionaire Sam Hardage is the leader over banker Dave Owen and state House Speaker Wendell Lady.

The biggest House race in Kansas is for the seat being vacated by Republican Rep. Jim Jeffries. Morris Kay, former GOP state chairman, is favored to win because he has name recognition, money and party friends.

In Missouri, Clay has the support of St. Louis' top Democratic leaders and of organized labor in a strong union area. He again should run up big votes in the largely black North St. Louis area, which is his power base.

But shrinking city population resulted in the dilution of that base and his district has been extended farther into the predominantly white--about 60 percent--and more conservative suburbs.

Mueller, who is white, is a 12-year veteran of the Missouri General Assembly and has strong party backing in the suburban areas.

Mueller has run a tough campaign, charging that Clay has been stricken by the dread Potomac fever and forgotten his district, and for his foreign travel on congressional junkets (19 such trips in 14 years).

Clay has responded by charging Mueller with ignoring the real issues such as the economy for "petty accusations about travel and missing quorum calls."

Race has not been an open issue in the campaign except for Clay's calls for heavy black voter turnout to preserve a black-held congressional seat in Missouri.