Ideally there should be no conflict between movements to establish, defend and strengthen democratic rights and the movement for socialism. Socialism, understood as common ownership and democratic control of the means of production in the interests of the community, is a natural extension of democracy from the narrow sphere of politics to the whole of social life (and in particular, of course, to the economy). That is why an alternative term for "socialism" is (or used to be) "social democracy." Political democracy is also a prerequisite for the effective spread of socialist ideas and for a peaceful transition to socialism.
In practice, movements for democratic rights often get mixed up with causes that are antithetical not only to socialism but also to democracy itself. This happens in two different ways, depending on the type of regime that is suppressing democracy in a given country.
In countries where the anti-democratic forces rely on the backing of the US and other Western powers -- above all, in Latin America, e.g. Honduras -- the democratic movement is prone to fall hostage to the "struggle against US imperialism" waged by other dictatorial regimes that are at loggerheads with the US and its allies. Hence the warm relations between Chavez' government in Venezuela, which is still basically democratic, and the anti-democratic regimes in Cuba and Iran. Conversely, democratic dissidents under anti-Western regimes (Cuba, Iran, Vietnam, China, etc.) are easily fooled by the hypocritical Western propaganda in favor of democracy and human rights. Thereby people struggling for the same ideals in different places are set against one another and manipulated as pawns in the power game of world politics.
Democratic movements have weak defenses against such manipulation for two reasons. First, people suffering under intense repression understandably feel vulnerable or even helpless and look for help wherever they can find it. They may not be sufficiently suspicious of the motives of those who are so generous -- and selective -- in offering their "support" to struggling democrats. Why look a gift horse in the mouth? And second, they may be poorly equipped intellectually to analyze the motives of foreign "benefactors." The same people who understand the politics of their own country very well and exhibit a healthy cynicism in the domestic context may be terribly naive when it comes to the politics of a foreign country with a system rather different from that with which they are familiar. Or they may simply not care: all they care about is the situation at home and they view the rest of the world solely from that angle.
As a result, even if -- with assistance from foreign anti-democratic forces -- democratic activists succeed in overthrowing one form of oppression, all they will end up with is oppression in a slightly different form. The only way out of the trap is for them to broaden their horizons beyond national and bloc confines and reach out to those "on the other side" who work in a different context and use a different political language but nonetheless share their deepest aspirations.