The experts in mathematical philosophy disagree about whether or not you need to be a mathematical realist to consistently describe the world using mathematics. Henry Jacob says, is poetic nominalism a thing? This would be a nominalist who moves through the world kind of like a poetic naturalist. For example, she would believe that chairs are not real but are still a valuable concept and it's a good idea to act as if they are real in many domains. As an applied mathematician, I find myself leaning towards something like this since I use models all the time and they're useful enough even though they're not real, I literally make them up.