Over the course of the FLDS-Texas debacle it became somewhat common to hear commentators finding in LDS support for the civil and familial rights of the FLDS a kind of holy envy. Much as reformed Jews are often characterized as having deep respect for the Orthodox who keep all the mitzvot, we were occasionally portrayed as having some sort of buried respect and nostalgia for the patriarchy and pedophilia of the FLDS (which, in turn, may cause one to question the nostalgia of our detractors, but that is another topic).
I would suggest that our vigorous objections to the manner in which Texas Child Protective Services behaved comes from several sources, not a one of which consisted of our collective secret desire for unclipped hair. Instead, I think that there are two fundamental motivations behind the LDS defense of the FLDS.
First, most American LDS actually believe protections established by the US Constitution. As victims of governmental abuse in the past, we do not delight in seeing any particular group suffer under the unconstitutionally-invasive thumb of tyrannic government. While I doubt our own history in this regard is spotless, I nonetheless believe that, for US Mormons, most of the outrage was grounded in our own history of persecution and government intrusion.
Second, I think that most LDS in Utah were happy to have the justification provided by the Texas Court of Appeals for the approach taken toward the FLDS in Utah and Arizona. Many times over the course of the raid and hearings, comparisons were drawn between the Western and Texan methods. Implied in many of these comparisons was that the sort of sympathy I alluded to earlier is what motivated the Mormon Utah Attorney General (and, somehow, the non-Mormon Arizona Attorney General) to approach crime amongst the FLDS with restraint, as opposed to a desire to actually only punish those engaged in harmful acts. The ruling of the Texas Court of Appeals adds weight to this interpretation. Restraint in approaching isolated peoples is a self-evident good; it does not and should not require additional justification.
So, it would appear that, unless you consider the judges of the Court closeted polygamists (have their TVs been checked for old episodes of Big Love?), that it is possible to grant those nasty old men and their child brides some rights without secretly wanting to start a compound yourself. I myself have been saving up my sympathies for the inevitable raids on the Strangite compounds in Wisconsin.