Do what feels right for you. If you want to refrigerate it for a cooler, firmer texture, great. If you leave it out for convenience, also great. Coconut oil is forgiving.
The only real no-no? Storing it near a hot stove or in direct sunlight. That’s like putting a snowman in a sauna—pointless and messy.
So go ahead, open that jar, take a sniff, and decide. You can always change your mind later. Coconut oil isn’t judging you. It’s just happy to be used.