I recently started selling my clothes at fetish websites and my parents found out about it while I was at college. My father was more disappointed with the guys that visited my profile and sending me messages. My parents want to ground me by taking my computer away for a few months. I'm an adult now and I don't think my parents should still be grounding me anymore. I pay for my transportation, food, cellphone bills, tuition fees, in addition to paying my part of the rent.

It's September - are you finished with college, but living with your parents?
I personally see nothing to apologize about, nor do I feel that there is any 'trust' that was lost. It was none of their business, except a bit in that grey area of using your computer (that they bought?) at their house on their dime.
So move out, or apologize just for the sake of keeping the peace in the household.
I would move out. I just don't see what trust was lost so I don't see what trust is to be regained.
I have no interest in selling my used underwear, but I see countless such sales going on on eBay, and if you can make enough (along with a regular job) to get your own place to live or a roommate situation, that's what I would do.
Your choice.
(BUT don't get personal with any of your buyers! DANGEROUS! )

I'm just wondering if all you bills are covered, why did you end up on fetish sites selling your clothes in the first place?

They probably are concerned that you are attracting pervs. Many parents say 'you live under my roof, you abide by my rules'. So as Joy said you can move out.