In response to a request, I am going to do some basic unpacking of second-order desire, or "metawanting". Basically, a second-order desire or metawant is a desire about a first-order desire.
Example 1: Suppose I am very sleepy, but I want to be alert. My desire to be alert is first-order. Suppose also that there is a can of Mountain Dew handy. I know that Mountain Dew contains caffeine and that caffeine will make me alert. However, I also know that I hate Mountain Dew1. I do not want the Mountain Dew, because I know it is gross. But it would be very convenient for me if I liked Mountain Dew: then I could drink it, and I could get the useful effects of the caffeine, and satisfy my desire for alertness. So I have the following instrumental belief: wanting to drink that can of Mountain Dew would let me be alert. Generally, barring other considerations, I want things that would get me other things I want - I want a job because I want money, I want money because I can use it to buy chocolate, I want chocolate because I can use it to produce pleasant taste sensations, and I just plain want pleasant taste sensations. So, because alertness is something I want, and wanting Mountain Dew would let me get it, I want to want the Mountain Dew.
This example demonstrates a case of a second-order desire about a first-order desire that would be instrumentally useful. But it's also possible to have second-order desires about first-order desires that one simply does or doesn't care to have.
Example 2: Suppose Mimi the Heroin Addict, living up to her unfortunate name, is a heroin addict. Obviously, as a heroin addict, she spends a lot of her time wanting heroin. But this desire is upsetting to her. She wants not to want heroin, and may take actions to stop herself from wanting heroin, such as going through rehab.
One thing that is often said is that what first-order desires you "endorse" on the second level are the ones that are your most true self. This seems like an appealing notion in Mimi's case; I would not want to say that at her heart she just wants heroin and that's an intrinsic, important part of her. But it's not always the case that the second-order desire is the one we most want to identify with the person who has it:
Example 3: Suppose Larry the Closet Homosexual, goodness only knows why his mother would name him that, is a closet homosexual. He has been brought up to believe that homosexuality is gross and wrong. As such, his first-order desire to exchange sexual favors with his friend Ted the Next-Door Neighbor is repulsive to him when he notices it, and he wants desperately not to have this desire.
In this case, I think we're tempted to say that poor Larry is a gay guy who's had an alien second-order desire attached to him via his upbringing, not a natural homophobe whose first-order desires are insidiously eroding his real personality.
A less depressing example to round out the set:
Example 4: Suppose Olivia the Overcoming Bias Reader, whose very prescient mother predicted she would visit this site, is convinced on by Eliezer's arguments about one-boxing in Newcomb's Problem. However, she's pretty sure that if Omega really turned up, boxes in hand, she would want to take both of them. She thinks this reflects an irrationality of hers. She wants to want to one-box.
1Carbonated beverages make my mouth hurt. I have developed a more generalized aversion to them after repeatedly trying to develop a taste for them and experiencing pain every time.
Let me try using an extended metaphor to explain my point: Remember Eliezer's essay on the Pebblesorters, the aliens obsessed with sorting pebbles into prime-numbered heaps?
Let's imagine a race of Pebblesorters that's p-morality consists of sorting pebbles into prime-numbered heaps. All Pebblesorters have a second-order desire to sort pebbles into prime-numbered heaps, and ensure that others do so as well. In addition to this, individual Pebblesorters have first order desires that make them favor certain prime numbers more than others when they are sorting.
Now let's suppose there is a population of Pebblesorters who usually favor pebble heaps consisting of 13 pebbles but occasionally a mutant is born that likes to make 11-pebble heaps best of all. However, some of the Pebblesorters who prefer 13-pebble heaps have somehow come to the erroneous conclusion that 11 isn't a prime number. Something, perhaps some weird Pebblesorter versions of pride and self-deception, makes them refuse to admit their error.
The 13-Pebble Favorers become obsessed with making sure no Pebblesorters make heaps of 11 pebbles, since 11 obviously isn't a prime number. They begin to persecute 11-Pebble Favorers and imprison or kill them. They declare that Sortulon Prime, the mighty Pebblesorter God that sorts stars into gigantic prime-numbered constellations in the sky, is horribly offended that some Pebblesorters favor 11 pebble piles and will banish any 11-Pebble Favorers to P-Hell, where they will be forced to sort pebbles into heaps of 8 and 9 for all eternity.
Now let's take a look at an individual Pebblesorter named Larry the Closet 11-Pebble Favorer. He was raised by devout 13-Pebble Favorer parents and brought up to believe that 11 isn't a prime number. He has a second order desire to sort pebbles into prime-numbered heaps, and a first order desire to favor 11-pebble heaps. Larry is stricken by guilt that he wants to make 11-pebble heaps. He knows that 11 isn't a prime number, but still feels a strong first order desire to sort pebbles into heaps of 11. He wishes he didn't have that first order desire, since it obviously conflicts with his second order desire to sort pebbles into prime numbered heaps.
Except, of course, Larry is wrong. 11 is a prime number. His first and second order desires are not in conflict. He just mistakenly thinks they are because his parents raised him to think 11 wasn't a prime number.
Now let's make the metaphor explicit. Sorting pebbles into prime-numbered heaps represents Doing the Right Thing. Favoring 13-pebble heaps represents heterosexuality, favoring 11-pebble heaps represents homosexuality. Heterosexual sex and love and homosexual sex and love are both examples of The Right Thing. The people who think homosexuality is immoral are objectively mistaken about what is and isn't moral, in the same way the 13-Pebble Favorers are objectively mistaken about the primality of the number 11.
So the first and second order desires of Larry the Closet Homosexual and Larry the Closet 11-Pebble Favorer aren't really in conflict. They just think they are because their parents convinced them to believe in falsehoods.
Again, I assumed that Mimi was a psychologically normal human who had normal human second order desires, like having friends and family, being healthy, doing something important with her life, challenging herself, and so on. I assumed she didn't want to use heroin because doing so interfered with her achievement of these important second order desires.
I suppose Mimi could be a mindless hedonist whose second order desires are somehow mistaken about what she really wants, but those weren't the inferences I drew.
Again, recall my mention of a hypothetical Heroin 2.0 in my earlier comment. It seems to me that if Heroin 2.0 was suddenly invented, and Mimi still didn't want to use heroin, even though it no longer seriously interfered with her other important values, that she might be mistaken. Her second order desire might be a cached thought leftover from when she was addicted to Heroin 1.0 and she can safely reject it.
But I will maintain that if Larry and Mimi are fairly psychologically normal humans, that Mimi's second order desire to stop using heroin is an authentic and proper desire, because heroin use seriously interferes with the achievement of important goals and desires that normal humans (like Mimi, presumably) have. Larry's second order desire, by contrast, is mistaken, because it's based on the false belief that homosexuality is immoral. Homosexual desires do not interfere with important goals humans have. Rather, they are an important goal that humans have (love, sex, and romance), it's just that the objective of that goal is a bit unusual (same sex instead of opposite).
EDITED: To change some language that probably sounded too political and judgemental. The edits do not change the core thesis in any way.
Your example does an exemplery job of explaining your viewpoint on Larry's situation. To explain the presumed viewpoint of Larry's parents on his situation requires merely a very small change; replacing all occurrances of the number 11 with the number 9.
How do you define objective morality? I've heard of several possible definitions, most of which conflict with each other, so I'm a little curious as to which one you've selected.