When thinking about this issue, believers must beware of falling into the post hoc ergo proctor hoc logical fallacy. We also need to beware of the you probably think this song is about you fallacy. See Simon, Carly, You're So Vain (1972). Just because we do or say something before an event occurs does not mean we caused the event to occur.
I can think of relatively few major doctrinal changes the Church has made over the years - and for the two big ones that come to mind, it seems clear that the change ultimately came because God commanded the change, not because the leaders of the Church succumbed to political pressure.
Official Declaration 1
By the time the Church began the process of ending the practice of polygamy in 1890, the federal and several local governments had already spent decades aggressively pressuring the Church to end the practice. The Republican Party listed polygamy alongside slavery as twin barbarisms it pledged to abolish. Church members and leaders were arrested, prosecuted, and imprisoned. Congress passed laws authorizing federal officials to strip people who practiced polygamy from traditional legal rights. Congress abolished the Utah territorial government. And the US Supreme Court upheld a law that, among other things, authorized the government to take Church property without compensation. This topic has filled volumes, and I will not discuss it at length. But (it should be) needless to say that if the Church's decision to end polygamy was simply meant to put an end to the legal and political pressure, the decision came decades too late.
There is no doubt that most revelation arrives wrapped in a cultural context. That is because revelation generally comes in response to a question or problem. But the revelation itself comes from God, and He decides the revelation's contents.
President Wilford Woodruff spoke at length about his 1890 manifesto. At one meeting, he reviewed with the audience all of the consequences that would have come about had the Church continued to practice polygamy, and then he made this crucial statement:
But I want to say this: I should have let all the temples go out of our hands; I should have gone to prison myself, and let every other man go there, had not the God of heaven commanded me to do what I did do; and when the hour came that I was commanded to do that, it was all clear to me. I went before the Lord, and I wrote what the Lord told me to write.
The Church would not have stopped practicing polygamy had God not commanded the end of the practice. God had commanded the practice in the first place, and no amount of political or legal pressure could have made the Church end the practice - only God could end it.
Official Declaration 2
By any calculation, 1978 would be a late date to arrive to the American civil rights movement. And the Church supported political and legal civil rights long before the majority of the country did. These are both reasons why it does not make sense to think of the decision to extend the priesthood to all worthy male members, regardless of race, as simply a concession to social activism or a calculation to join the mainstream.
For an exhaustive treatment of this subject, including an appendix containing official Church statements, go here.
For years, the Church's First Presidency was pressured to simply extend the priesthood to all men (and, by some, to all women) regardless of race. President David O. McKay (1951-1970) reportedly felt sad (along with most members of the Church) that the priesthood was denied to so many. Had the decision been a matter of mortal administrative preference - he very likely would made the decision. But in 1969, the First Presidency issued a statement to clarify the following:
From the beginning of this dispensation, Joseph Smith and all succeeding presidents of the Church have taught that Negroes, while spirit children of a common Father, and the progeny of our earthly parents Adam and Eve, were not yet to receive the priesthood, for reasons which we believe are known to God, but which He has not made fully known to man....
Until God reveals His will in this matter, to him whom we sustain as a prophet, we are bound by that same will. Priesthood, when it is conferred on any man comes as a blessing from God, not of men.
We feel nothing but love, compassion, and the deepest appreciation for the rich talents, endowments, and the earnest strivings of our Negro brothers and sisters. We are eager to share with men of all races the blessings of the Gospel. We have no racially-segregated congregations.
Were we the leaders of an enterprise created by ourselves and operated only according to our own earthly wisdom, it would be a simple thing to act according to popular will. But we believe that this work is directed by God and that the conferring of the priesthood must await His revelation. To do otherwise would be to deny the very premise on which the Church is established.
Just as with Official Declaration 1, no amount of political or legal pressure would have generated Official Declaration 2. Several presidents had prophesied that the Lord would eventually extend the priesthood to all men. But that decision was God's to make - not the president's.
When it comes down to it, we can lobby for doctrinal changes. But we must lobby the right Person through prayer - He's the one who can give us what we're after. When we pressure the Church's leaders to change doctrine, we're essentially barking up the wrong tree.