Let me throw in my advantage in actual experience at the way the Church handles these cases, namely 'homosexuality'. I have personal witness to members who had these tendencies and even made moves on other members of the same sex in Church and have very little done to them. I have even had to fight that some of these people not receive the Melchizedek priesthood since the other leaders seemed to place a blind eye on the threat they were to the membership.
Now, let me clarify something, I have no problem with gays, I had a few of them as good friends at one time, but I do have a problem with them making advances on other members and then being asked to participate in Priesthood ordinances. I once had a Brother as a home teaching companion who was gay. He went to the US to meet with the missionary who baptized him to profess his love for him (of course he no longer comes to Church). So yes, the Church looks at homosexuality very lightly. Interestingly enough, I have always seen the focus on the Brethren, but who knows how many Sisters in the Church may also have Lesbian tendencies and not say anything.
Conversely, when you talk about Plural Marriage everyone sits up in their seat, they get defensive and start to vehemently deny any kind of participation of it in Church history. Most will try to tell you that it was just necessary in order to cross the plains, in fact, my parents were rigidly told this in Utah, where we once lived, as the reason Plural Marriage was started. Another common mistake is that most assess Brigham as the instigator of it and so 'pardon' Joseph for it, but this of course is not true. In all honesty, I have seen many a 'gay' looking, sounding and acting person in Church with no questions asked (no I am not stereotyping), and many a person trying to discuss things like Plural Marriage being told basically to 'stop asking'.
I think the issue is one of intent. I do not condone either Homosexuality nor do I condone Plural marriage without the sanction of the Lord.
But Homosexuality deals with urges that seem to not have a outlet. I would assume that if one has very strong feelings for someone of the same sex, changing that desire is very difficult. I think this is why there is some compassion for those who have these feelings.
Those who have proclivities for members of the opposite sex are able, under the current law of both God , practice these urges within the bounds of marriage.
Were as someone who is homosexual must change a part of their nature to comply with God's law, the same is not necessarily true for the Polygamist. He or she is able to practice their heterosexual proclivities within a monogamous marriage. The man or woman who is Homosexual has no equivalent outlet.
President Hinckley, while talking about homosexuality, was talking about them as a whole "love the sinner, hate the sin". Yet while talking about Polygamy the Church has a past with it, and he wanted to make sure that it was clear that we don't practice it, or allow others to practice it ether. The Church never has, and never will accept homosexuality, it is purely of Satan, yet polygamy has been a doctrine of God. President Hinckley was not talking about homosexuality within the Church, but he was when talking about polygamy.
I have seen the same leniency towards homosexuality here in Provo at BYU. The mother of my sister-in-law worked in house keeping and noticed people, well, acting out their urges towards the same sex (in the womens areas at least, but I would think that it's not necessarily different in the mens housing), without them getting disciplinary action from BYU whatsoever. Whereas if a man belongs to a "polygamous" group, he get's kicked out as number one on the day's to-do list. He doesn't even need to act on it.
A homosexual convert can be baptized after a few interviews with a stake or mission president, even before he conquers his "urges." Whereas I had a friend who was part of the Apostolic United Brethren and his parents lived Celestial Marriage. He was wanting to join the LDS church as he felt he couldn't live up to the requirements in the priesthood work. When he wanted to join, he had to take institute for a few months, had semi-weekly interviews with Bishops and Stake presidents and had to meet with an apostle to get "cleared" for baptism (in his case Elder Holland), and of course had to deny that the doctrine of Patriarchal or Plural marriage was in any way, shape or form related to Celestial Marriage (as defined in moder times), and that he could find salvation only in monogamy. If a polygamous African wishes to join the church, he is REQUIRED to divorce part of his family, and disown all of his children by the divorced wife/wives before he can be baptized. Even though he married them completely legally, and it is completely legal in his country to live that way, totally ignoring the fact that Official Declaration-1 merely suggests not marrying plurally were it is illegal, and isn't addressing countries where it is legal at all.
So looking at what I see from the church, I think it is definitely much harder on people trying to live plural marriage than it is on homosexuals. And yes, I do think that is related to social pressure. I think it's similar to the times of the civil rights movement, when the church was being so heavily criticized for barring Africans from the priesthood and they changed some church policies to to seem less offending.
About "Polygamy" being a doctrine of God, I beg to differ. Celestial Marriage, or patriarchal marriage, is a doctrine of God that necessarily includes a plurality of wives. Polygamy differs as it is not heavenly binding, nor is it limited to a man having wives (polygamy means multiple marriages, regardless of the sexes or sex distribution involved) as the only form of plural marriage that has divine sanction.
The whole scenario with this and the Church is that the Church wants to favor what the government wants just as they did with Polygamy. The governments largely want to favor homosexuality but not plural marriage. This may just a case of welfare. With plural marriage you have many children coming on welfare, school, etc. With homosexuality the population stops there unless they adopt and usually it is just one.
I don't think either can be considered worst than the other except that Polygamy once existed as ordained of god and homosexuality never was.