Evil? We're SAVING the world!
No one thinks they're the villain. Outside of a few very adolescent power fantasy type cults, nearly every other cult is based in imagining it's doing something for either the greater good or at least the good of it's members, and has rationalized all the things it has to do in that regard.
Sacrifice a baby? The baby was evil & deserved it / by killing the baby we actually set it's soul free / the world would end if we didn't / the parents have wronged us and we're stealing the baby's power, they deserve it / it's not even a real baby anyway, this is all a test by (deity), etc.
Cults run on hope, but are backed by social pressure
All cults promise something. They promise something the general society doesn't offer, and most of the time it's some form of secret power, knowledge or salvation. "The rest of the world will fall like fools because they couldn't see the TRUTH. The truth only WE know. You and I? We'll be like gods, while THEY burn! You are wise to join us!" etc.
It appeals to the desperate and secretly greedy.
Once people are in, eventually more and more commitments are requested, and the way to keep people in is the social pressure. They try to cut people off from their families or bring the whole family into the cult itself and then cut people off from social backing outside of the cult (except when, say, they're using those same connections, like a politician or celebrity). They find out secrets, they threaten and blackmail, but it's always under the guise of having to fulfill their dream, the person being "corrupted by the world", or having to protect their own.
The greater the isolation, the deeper the fanaticism goes, and the more extreme the acts of violence and abuse become because people have become normalized to it and their lines of what's reasonable are further and further astray.
Leaders are charismatic
To sell this line of hope and dreams, and to rationalize all the abuse, the leaders are charismatic. Either they're the form of salvation itself, or they're the one everyone wants to be, or be with. These leaders are very good at playing people against each other, using social bullying, rumors, and lies to keep the cult busy and obeying rather than simply fact checking with each other and realizing they're all getting played.
As much as the sexual abuse might be enacted from the leader, there's also a lot of people who will throw themselves, or offer up their partners, or even children to the leader to win favor. It's pretty much the most horrific end result of transactional thinking applied to salvation.
The cult you get when you first join is not the cult you get when you're in deep. The frontward facing side of cults focused on recruiting is often no different than many other religions. There may be a few doctrinal differences, but otherwise, it's a fundraising and general recruitment pool.
Those who seem especially dogmatic or eager to throw their energy in, or, those who are willing to buy their way in and meet higher and higher cash requests, will be recruited deeper in.
It's harder to say if the fanaticism is a requirement to push the more violent, abusive and bizarre behaviors, or if, even left with relatively normal, vague commandments, fanatics will just find a way to make it violent and abusive anyway. We can see extremists of any religion take it there no matter what the original values taught were...
Taking it to fantasy
The big difference in fantasy is that religious elements are more immediately "provable". You can do magic or you can't. You can summon spirits, or you can't. This isn't a perfect set up, since, once you HAVE magic operating in your world, the reason WHY magic works and what it means theologically can be faked or rationalized a thousand ways.
A wizard with no ties to any deity or philosophy could easily pretend all their powers come from a deity and form a cult. A trickster cleric could pretend to get his powers from another god or power. etc. A ritual might always fail not because it's bullshit, but because "you haven't earned the god's favor, yet."
The other side of it is because magic is real, depending on how rare/common it is, how much people are desperate for that power or what it might promise, people are extremely motivated and possibly more vulnerable to a cult's offers.
If you have a game where magic cannot raise the dead, maybe cults form around seeking this. If you have a game where magic CAN raise the dead, maybe high end members regularly die and are brought back to "earn piety"!!!
All in all, if you're taking real world cults and putting it in your fantasy, just realize they mostly come down to money, sexual favors, and sometimes political push, such as ethnic supremacy cults. Even if the magic exists to (travel to another world, summon their god, etc.) most of the cults actually won't try to really make that happen, instead using it as a carrot to keep the cult itself wasting their energy while bleeding off on exploitation.
This also means that even jaded and well informed people will probably dismiss most cults as anything other than a minor social evil, outside of their abuse and occasional acts of public violence. So, if a cult actually DOES start tapping into real evil powers, just about everyone will be surprised by it...
(Also this means you will see violent fanatical cults supposedly dedicated to good deities as well, which sets up interesting roleplaying conflicts...)