By proper Catholic definition, no.
By the common definition as used in the world, yes.
By the definition of most Protestants, yes, and some would even say Catholics are not Christians.
Most of what we are exposed to in the world considers Protestants Christians.
Exactly.
Sometimes terms are not technical theological words but can be used in different contexts.
If you're not a Muslim, not a Jew, not a Hindu, not an atheist, than, what are you? Typically you say "Christian" in a looser, more colloquial sense to mean ... NOT one of these other things. If you just keep saying ... "a non-Christian heretic who nevertheless self identifies as a Christian", it would get rather tedious, and people can infer your meaning from context.
But as a theological definition, no.
As I said, though, in the early Church "catechumen" was consider "Christian" already even if not a formal member of the Church, whereas then "Christian" was divided between "faithful" and "catechumens". So there's yet a third meaning where it's not co-extensive with a member of the Church, but its just a bit broader, to include catechumens who have a least professed their belief in the Catholic Church.