I think the discussion has been distracted by a red herring. It's not about whether the site is family-friendly or should we be offended, etc. The question is really about whether using profanity helps in a forum for technical computer assistance or not.
Most things aren't neutral; they either help or detract from the overall mission. Sometimes people ask why others are such grammar-nazis and try to create a debate about whether it's wrong or right to correct people's grammar, spelling, and punctuation. Just like here, that's the wrong topic for discussion. Those things help make questions and answers clearer and more useful. That's why people do it. Or at least, that's why people should do it.
To use an example in the question, does it really help to describe a system as "fucked up"? Isn't it better to actually describe the situation in a less vague manner? Like "I only get a blank screen"? Of course, the person asking may get to these details later, but my point is, does throwing in profanity usually make things clearer? In my experience, profanity doesn't. We're talking about computer stuff. Would you rather have "Don't use this command or it will fuck up your account" or "Don't use this command because it will delete your access to the account, although all data will remain and is actually backed up daily." Again, maybe someone saying the former will eventually get to the usual info, but we should value conciseness. Get to the point. We don't need a prelude of profanities to the actual useful info and we certainly don't need profanity laced into the useful info.
This also highlights another problem with profanity. Usually it indicates a lack of control on the part of the speaker. It suggests the person is letting emotion get the better of them and that the advice is somehow less objective. Now, some people, I'm sure, think they just use profanity everywhere unemotionally, e.g. "Would you fucking like to eat some fucking cereal? We have fucking Cheerios and fucking Fruit fucking Loops." Yeah ok, fine. Such people have entirely forgotten the point of profanity. Since most people have not, communication is now fraught with potential for misunderstanding. For example, I could take the neutral statement about cereal and believe that the person thinks eating cereal is stupid or that they don't like Cheerios. Such confusion is natural when profanity is now being used generically for no purpose other than to fill in pauses in a sentence.
To make a long answer short: yes, profanity does "change the quality or usefulness of the help I provide". Give me an example of the help you provide and I am pretty sure I can improve the quality by removing things like "the system is fucked up" and replacing it with something clearer.