There is no concept of non believer in the dharmic faith systems, everyone is allowed to have their belief systems and one faith doesn't impinge on others belief or faith. So, the concept of taking a life for that does not exist.
The whole concept of "is taking a life okay for dharma" means something else. Dharma does not mean religion. In fact the specific example of Bhagvad Gita is, a warrior prince is in doubts about fighting his cousins for his kingdom because it will lead to bloodshed. It is mentioned as he is a prince it is his duty to fight for his kingdom, this is alright.
An example for this will be, if in the current Russia Ukraine conflict Russia invades Ukraine; it is in the dharma of the Ukraine's military to fight them even if it causes bloodshed. However, the whole concept of Dharma and how a battle should be conducted would forbid some things that you actually end up seeing in real world conflicts.