I could see both a female Indiana Jones and a female James Bond.
Indiana Jones is just a smart archaeologist who kicks ass. Look at The Last Crusade and Elsa, she is basically his equal is she had a little better head on her shoulders (and a little more physically impressive which another actress could pull of [say Charlize Theron], just not Alison Doody).
James Bond uses sex as a weapon, why couldn't a woman do the same? The rest of it is just dedication to Queen and country and some ass kicking.
I can understand why some people would be so connected to the gender of a character, but I think it in no way would "ruin" the mythos of a character if gender were recast.