Certainly, some people are deluding themselves. If a person makes up their mind on a subject prior to even seeing the evidence, he is hardly a skeptic no matter what he wishes to call himself.
And while there are people who are legitimately skeptical - there are others who clearly have made up their minds, as evidenced by their willingness to accept any stupid claim offered and promulgate that claim without doing any critical thinking on that claim themselves. The person can call himself the Virgin Mary, but it doesn't make him a skeptic.
A person can approach a subject skeptically and then become convinced by the evidence. Still, the person is a proper skeptic, if not on that subject - at least he examined the evidence prior to developing an opinion. There are those who make up their minds and then demand unreasonable evidence for the contrary, but accept (and repeat and repeat and repeat) literally any stupid claim they happen to hear that appears to agree with them. Again, the person may call himself a skeptic in the same way that mob boss might call himself a businessman.
