If you choose to engage law enforcement personnel, it's "thank god, some extra protection" (hopefully!), but if there is a situation where law enforcement personnel engage you, it's either "huh?" or "oh fuck". This isn't different for the FBI than for local or state-level police.
If some law enforcement personnel show up that you didn't invite, they could be there for a large number of reasons. How worried you'll be depends on how likely you think they are to do what they're supposed to do instead of what they're not.
If they're canvassing for witnesses, are they going to charge through your yard and shoot your dog? If they're investigating someone else, how likely are they to try to come up with something unreasonable to charge you with for leverage and then make you plead it down to a penalty that still isn't zero in exchange for giving them information you might not even have and would then be forced to choose between fabricating to get the deal and "not cooperating" and getting a serious prison sentence?
If someone is attempting to SWAT you, how likely are they to ascertain the situation instead of shooting first and asking questions later?
If their investigation has led them to you for some reason even though you're innocent, do you expect them to care about the truth or just railroad you?
If you hear the name of a particular law enforcement agency unexpectedly when you don't have any reason to think you've done anything wrong and your instinct still has to be "oh fuck" then they're bad at their jobs.
I think most people would have essentially the same reaction to either FBI or state/local police showing up at their door with "[Police|FBI], open up!", and it depends more on whether they believe they've done something illegal than the reputation of the agency. This was my disagreement with GP(stavros).
Depending on how you expect the reader to answer all your questions, we could still be in full agreement, but my sense is that you're asking them rhetorically?
You can ask the same questions about a local law enforcement agency but the answers won't be the same for every one of them.
And then in terms of literal sentiment, most people aren't familiar with any given local law enforcement agency because there are so many of them, so they wouldn't know what to think, and some of them are quite bad. But the knowledge of the average person it isn't really the point.
Suppose you actually were familiar with the record of whatever specific agency just showed up. If you would still have to think "oh fuck" then they suck.
If this was true, the Miranda rights would read something like “anything you say will be used to obtain justice” rather than “anything you say can and WILL be used AGAINST you.” The police and justice system are never your friend. They are always your adversary, and should be treated as such. Under a different regime, they could be your ally if you’re innocent, (and this is the case in many countries) but in the US, they are always hostile to everyone, including innocent people. Even if individuals in that system don’t fancy themselves in that light.
I engaged law enforcement personnel as the victim of a violent (unarmed) home invasion robbery by people I knew. What did they do? Debate whether I should have been arrested instead on a technicality. That would look good for their stats, right? At least the criminals had to repay 90% of my lawyer's fees.