As far as I know, the only subject in which it's okay to take a "non-majors" course is physics. And even then, it needs to be a serious course, just not calc-based. (Some schools, I know, have classes specifically called "physics for non-majors" but it's all fluff, just helping people to understand generally how the world works, without the problem sets, etc.. That is not the same as the non-calc-based physics classes we're talking about.)
In most cases, all of the prereqs need to be of the type med schools would accept... which in chemistry and bio need to be the same courses the majors would take. (I suspect the reason a physics for non-majors course is okay is that physics for majors requires some serious math background, and yet even most med schools don't require calculus as a prereq, so it would be odd for them to expect people to take a physics course which requires that background... it would in essence be requiring calculus. Major courses in other science subjects do not require knowledge of calculus.)
Good thing the non-calc physics classes are okay! I took AP Calc in high school and then two calc classes in college, but I sooooo do not remember any of it over ten years later. A requirement to take a calc-based physics course would put meeting that prerequisite totally out of reach for me, and for a lot of people, even those who did take calc.