From time to time I see players play this move, which is not in theory books. Is 2.Bc4 really an attempt to sidestep theory or does it just transpose into a normal Sicilian opening? I have the feeling that it is a solid way to avoid Sicilian theory although I feel comfortable to play against it and I've never lost against this opening in correspondence chess. Normally I play 2...e6 3.Nc3 Nc6. Are there better responses?

It seems the B is exposed to attack with a gain of time for Black while expanding in the center or Q-side. It suggests to black …e6 and …d5. Also sometimes in the Sicilian it's better to delay the development of the f1 Bishop because Black has a lot of choices of pawn structure. Some of which may be better met with Bd3, Be2 or Bf1-g2, than with Bc4. The fact that it’s not very popular at the GM level suggests to me they know something the rest of us don’t.

Here is a link to a GM game showing how to meet it even though White played it at move 3 instead of 2.
Eduardo Arruda vs Vladimir Kramnik (1991)

I see this all the time, ...e6 and prepairing for ...d5 gives you the ideal break and equality or better.

True.

If you're lucky you'll get into some kind of Pelikan or whatever. Hardly what the players trying this move are looking for. It's been tried with 2. Nf3 Nc6 3. Bc4, same story.

Actually, 1. e4 c5 2. Nf3 d6 3. Bc4 isn't that bad, precisely because Black is a move slower playing ...e6 and ...d5. I'm not sure why this is attractive to players of the White pieces anyway, because Black has a number of comfortable transpositions if d2-d4 is played (notably the Sozin), and if White doesn't play d2-d4, then what?

My only draw against a 2300+ player came when they played:

1 e4 c5 2 Nf3 d6 3 Bc4. They played for c3, d4, but everything in the center ended up trading off and we just had rooks w/ even pawns at the end.

Probably not white's best try for an advantage.

There is minor sideline in MCO-14. It goes:
1. e4 c5 2. Bc4 e6 3. Nc3 a6 4. a4 Nc6 5. d3 g6 6. f4 Bg7 7. Nf3 Nge7 8. O-O O-O =

Black does has to be careful to not play ... d5 prematurely. He has to be very patient as prematurely opening the center could land Black in hot water due to White's piece activity.

Is not so much ...e6 and ...d5, which is more a matter of Black immediately taking over the initiative. It's a great plan, but it does require some forethought and calculation, and it isn't a solution on its own.

The problem is that after ...e6, White's bishop doesn't really serve a useful function on c4 anyway, and is a target for pawn advances (...b5 as well as ...d5) and trades (Nc6-a5, Nd7-e5). Black has any number of ways of acheiving equality, and if ...e6 and ...d5 doesn't work, then ...b5 and ...Bb7 will, or getting the two bishops by Nc6-a5xc4.

White doesn't have an obvious plan, and has a number of moves that are more flexible than 2. Bc4, notably 2. Nc3 and 2. f4 if White wants to play a closed game.