What I find weird is that certain episodes are given TV-14 ratings, but the TV-14 episodes don't have anything more mature then the normal TV-PG episodes, so I don't get why some episodes get that rating. Only episode I can think of that is really worthy of that rating is the recent 2 parter for its overly graphic realistic violence, which unlike the THOH's, the violence is typically more comedic then raunchy. As for it being for adults or not, I honestly doubt that, it's more of a family show since the humor is for all ages and it isn't specific to adults either because there is a lot of stuff that kids like in the show as well. Not little kids, but like 10 and up. Ain't no adult show compared to other stuff. It's in the same league as like Bob's Burgers, The Great North, and King Of The Hill to name a few.
Although as like what Financial Panther said, the show for a while did get more edgier and was being more mature like Family Guy if that makes sense, which primarily started after the shows decline, and this is when they constantly would have for example Homer and Marge wanting to fuck, and rubbing sex jokes in your face up the ass all just for the sake of just doing it I guess, and constantly using terms such as "intercourse", "hoe", "skank", and a few other terms like that which is totally out of tone for the series if that makes sense, as well as constantly mentioning drugs and just move away totally from the original smooth charm of the show that had very little innuendos, little and rare references to drugs or even showing them, but never has the show actually have shown any character doing the drug if present physically even in the long edgy period starting from about Season 14 to Season 20.
Around the start of the HD era is when the show eased down and wasn't trying to be edgy and more mature just for the sake of it, but still has the stuff I mentioned above, but not used in almost every single episode, but definitely still not the same tone as the Classic era and its charm, but still not as bad as Season 14 to 20 edgy era. Although the "Edgy Era" per say was trying to be more mature and more adult like such as Family Guy, it still was getting TV-PG ratings. Also if it was for adults only, why are they especially now trying to be hip with tweens and teens for the past 3 Seasons per say?