While it is obviously a complex Sugya, there are reliable opinions that allow one to use one oven for both Dairy and Meat, even consecutively, even uncovered. Many people rely on these opinions as they only have one oven in their homes. According to those opinions, would it be permissible for Kosher food to be cooked in a non-Kosher oven, assuming that nothing non-Kosher is being cooked at the same time and the oven is clean?
Use a non Kosher clean oven is worse than using one oven for both Dairy and Meat, so therefore it should be kashered before being used for Kosher food.
Rashbo Toras Habayis 3:4, Run Chulin 111, Ritva Chulin 112a, Taz Y:D 95:1, Pri Megodim O:CH 452:Eshel Avrohom 11, Beis Yosef Y:D 95