I think there are at least some philosophical topics which are non-objective by nature. Consider whether to be a solipsist. ;) More seriously, if you don't believe in an objective morality, then moral philosophy is a subject which qualifies.

Something that is non-objective by nature is a matter of faith, not philosophy.

I do believe in objective morality. Morality is simply the study of what we should do. What should we do? That question is perfectly open to scientific enquiry.

If Hume was right---that the question cannot be answered scientifically---then that's the end of moral philosophy and the beginning, perhpas, of morality based in faith. but I do not agree with Hume.