Surgeon Gen. C. Everett Koop, in his most explicit public comments on the prevention of AIDS, has asked the nation's physicians to recommend condom use for all sexually active patients unless they are certain their sex partners are free of the infection. "My moral and religious background has made it difficult for me, as it may be for you, to discuss sexual issues in public," Koop wrote in an editorial to be published in this week's Journal of the American Medical Assn. He added, however, that unusual frankness is necessary because the "alternative is almost-certain death." Koop has been the Reagan Administration's most vocal and persistent advocate of condom use to prevent transmission of AIDS. In his editorial he writes, as he has in the past, that condoms are not 100% effective, but "if correctly used they can dramatically reduce one's risk of exposure."