That is very much the case at some restaurants that consider food to be art. Art is different. To be able to appreciate and understand it, it's all or nothing.
I guess we'll have to agree to disagree. However, I know film is art, but movies are mostly watched for entertainment. Censoring entertainment seems totally fine to me -- I should be able to skip watching part of a baseball game if I want. Hell, it's MY mind and eyes -- why don't I get to control what goes in? Maybe I like 95% of something. Is that to be withheld because I don't like the other 5%?
I think the argument is that art is sort of a predictive negotiation: to go with the food analogy, most chefs just won't cook for you if they know you won't eat what they're making the way they've served it (e.g. if you cover everything in a flood of ketchup.) If you're not interested in the idea they're trying to communicate to you through the art, then they stop experiencing the self-actualization of communicating that idea, and instead feel like a commoditized provider of grist for you to construct your own experience from. That's not what they signed up for.
You absolutely do get to control what goes in, and I really don't care if people use this tool only for themselves. I think you will not have seen the work in question. I think you can not have understood it the same way that someone who saw the entirety of the work can understand it, and I would consider you to be a bit silly for wasting your time.
What do you feel you gain by excising the objectionable portions of a work?
I gain not being affected by it. My buddy loves masacre horror movies. They used to scare him and freak him out, but now he's numb and it's just entertaining to watch someone get chopped up. Sure it's not real, but the effect it had on him was real. I can't say this for certain (though I need to test it now) but I'll bet I respond in a much different way to real world violence than he does now. Your mind is affected by what you put in just like your body is affected by what you put into it.