A cultured person, in the European tradition, is one who is well rounded and Ranma is definitely well rounded, heck he is probably the most well rounded in skills in the manga displaying knowledge in a large variety of fields (cooking, cleaning, repair work, sewing, horse riding, first aid, CPR, some knowledge on magic, designing (he makes his own disguises in the manga; can be seen sewing a costume before the battle with Mousse - pictured above), tea ceremony, proper manners (though he doesn't always use them), animals, constructed spirit wards (didn't screw them up in the manga only in the anime), dancing (went dancing on a date in the manga), wrote a play and went to see plays), etc.
If you use word net's definition of uncultured that is lacking art or knowledge. Ranma is not uncultured by that definition either. Since he has displayed knowledge in many fields. Is passing in school and doesn't appear to have any trouble with his classes (in the manga, even the anime implies he is passing). As for art he has displayed creativity and imagination and has a superior skill that you can learn by study and practice and observation which are two definitions for art. Heck he even created and directed a play.
Ranma is not uncultured he is uncivilized. They aren't the same thing. One who may be poor and wearing cheap apparel may be considered 'uncivilized', but still he or she may be the most cultured person. Ranma does fit the definition for uncivilized in that he is often rude, doesn't use manners very much (though he does know them), and acts like a savage on occasion (swings - more like bounces - from tree to tree, howling at the moon, eating while crouching on the table, sleeping in trees). He doesn't fit the definition for uncultured.