Present-day scepticism sure has taken a turn for the worse, hasn’t it? There’s nothing particularly brave or interesting about debunking alien abductions, crop circles, psychics, miracles, etc. Most of that stuff debunks itself.
Try instead being sceptical about received notions. Be sceptical about what you think you know. And not just what you think you know about otherworldly phenomena (though, by all means, be sceptical about that), but also about everyday, ordinary things.
For instance, when someone asks how much stable institutions promote economic growth, the traditional assumption is that stable institutions must somehow promote growth of some kind (even if we don’t know how much), because states with long-term positive growth seem to have stable institutions. A sceptic might ask whether we’re creating a causation out of a correlation. Maybe the situation is the inverse, that states with long-term growth tend to generate stable institutions.
Or, for another example, you could be sceptical of the idea that science can explain everything. You can be sceptical, because this seems to be a worldview narrative instead of actual objective reality.
Or you could be sceptical of the ability of logic to describe reality, or at least to describe a reality that you’d want to live in.
Basically, take anything from the Enlightenment, and therefore from the Greeks, and be sceptical of that. The Enlightenment is the air that we breathe, the water in which we swim, and it’s important that we remember that despite the massive benefits of the Enlightenment (though, of course, we should be sceptical that these benefits actually flow from the Enlightenment), it’s not sacred. It seems like it is. And to some people, I suppose it actually is.
Fairies, ghosts, occult phenomena, and the appearances of angels and demons are the soft targets. They allow you to rationally debunk something with facts and logic, allow you to be lazy and superior, to get that us vs them rush, without having to do any really hard work. (See also /r/atheism.)
What I’m saying is if your scepticism is (in general) pointed at someone else, you’re using your so-called scepticism as an us-vs-them marker. If it’s pointed at someone else, then you’ve taken your first step toward the violence inherent in demonising (ironically in this case) the Other. If, on the other hand, your scepticism is pointed at yourself, the worst you can do is demonise yourself.