First off, I believe that true possession is rare.
1) Why would you want to analyze their minds?
natural curiosity -does the mind change when possessed and how does it?
I would kindly suggest being very careful and prayerful as to what you are curious about. I'm not saying it is wrong to be curious or know how the mind works, but there's an old saying about curiosity and the cat.
2) Considering your personal feelings of disgust towards such people, would you have the same feelings of disgust about people who were afflicted and visited by demonic sources? If not, please explain the difference.
Keep in mind saints such as Saint Gemma and Saint Pio were tormented in this way as well as priests.
Well that's a contradiction there: you should be disgusted by evil things (a devil in a body which uses said body for evil ends) yet you shouldn't be disgusted if a saint were possessed -I don't know how to respond to this. What do you think is the right attitude?
This is simply something I thought you should put some thought into...
3 ) I'm also curious how you would come across several or even a couple of possessed people? By the way you prosed your question, it comes across as if you've ran into this more than one time... Especially, if it has occurred often enough for you to seek and ask advice here regarding how to address these people. Clearly, you aren't employed by the church, or else you wouldn't have to ask how to treat such people. (nor would you have the feelings of disgust as we are told to love one another and treat all people with compassion)
a) not every catholic disgusted at someone is a bad catholic since hatred of a person's bad qualities but not the person is not bad, so much less is disgust at the same thing a bad feeling.
I don't believe anyone in this thread (aside from you) has used or implied the words, bad Catholic. I believe the concern was the use of the word, disgust, when speaking of people who are in a situation they have no control over. However, you could possibly run into the same thing when using the word hatred...
b) the word "generally" connotes an idea that I've been around a lot of these people when in fact I haven't. I used it to mean "for every time one encounters a possessed person".
Thank you for clarifying, several of the posters were concerned or curious about this