Should you get rid of all the stuff an ex gave you so your new partner doesn't feel bad?

Its your choice.If there are things you want to keep then you can keep them.Pack those items in a box for storing.Dont mention it to your new
partner.

Sometimes people might meet up with an ex in their lives.If people do this and they can chat then they might share memories.Then its a good time to tell them you kept various things.

Your idea is good.It shows you are considerate towards a new partner.Just dont deprive yourself of treasured memories.People do keep relationship items so dont throw them all out.