EDIT: This was typed at the same time as the above, nach. It isn't a reply to it!
The practical effect of Supreme Court decisions can massively change the impact of a law (in fact, sometimes their decisions have a greater effect than any individual law). If the Supreme Court finds the death penalty to be cruel and unusual punishment, presto--the death penalty is illegal, instantly, in every state. If they start broadly interpreting forth and fifth amendment rights, that has far more significant impact on criminal law than any individual piece of legislation--and, likewise, if they start interpreting it narrowly, a number of legal protections simply vanish, and police powers expand. When they made their decisions in Brown vs. the Board of Education and Row v. Wade, dozens of laws across the nation were suddenly unconstitutional and ceased to be legally enforceable. In the real world, for instance, the New Deal--the most 'liberal' agenda ever passed in the US--was greatly curtailed by the Supreme Court.
As a practical matter, Supreme Court decisions can gut laws entirely, grant or take away rights, and so on.
Free speech... we shouldn't hold an ideological debate here; the game is intended as dark humor. But to answer your questions from a liberal perspective: School prayer is antithetical to freedom of expression; officially establishing one religion interferes with people's rights to hold whatever religion they wish and raise their children under whatever religion they wish, which is a vital part of free speech rights. From a liberal perspective, people who want to force students to pray in school (or set up situations that could pressure them into praying in school) are the opponents of free speech.
'Hate speech' is much simpler, and much of it is a myth. There are no major liberal organizations or thinkers in the US that support the sort of 'hate speech' legal restriction on freedom of expression that you are referring to, even when saying things that are hateful. The ACLU--the core of liberal free-speech support--has defended the free-speech rights of neo-nazis, often against conservative efforts to silence them (and have been ridiculed by conservatives for doing so.)
Now, there are a few things to note in that. First, freedom of speech does not mean that you are free from the social consequences of your speech... if you use your freedom of speech to say stupid or offensive things on TV, everyone else is free to use their freedom of speech to criticize you. Second, freedom of speech is not freedom of forum... you have a right to express any opinion you want, but you don't have an automatic right to a TV show on MSNBC; people who mail hundreds of letters to the head of the station complaining that they hate your show is not a violation of your right to free speech (it's closer to the free market at work.) There are problems inherent in this, naturally; they were more serious during the broadcast age, when 'forums' on TV were limited by the available range. During that time, liberals supported the Fairness Doctrine to ensure that minority or hated viewpoints weren't totally shut out by social or market pressures, while conservatives opposed it. With the rise of the internet this has become less important; Toady could kick us off of this forum if he didn't like what we said, but nobody could seriously argue that that affects our free speech rights.
Hate crime legislation is another issue many people bring up, but, again, from a liberal perspective this doesn't actually touch on any issues related to free speech; free speech doesn't extend to expressing yourself in ways that are otherwise illegal. It would be absurd, for instance, to argue that killing someone because you hate their race is a protected way of expressing your hatred of that race.
The key here is that hate crimes are about the nature of the crime. The principal of taking motives and the murderer's state of mind into account is long-established in criminal law; premeditated murder is more serious than murder in a fit of rage, while murder in 'justifiable' rage is less serious than murdering someone because they dropped a spoon. One of the most harshly-prosecuted categories of murder defined in law is assassination, killing someone for money, since the financial incentive carries widespread risks if not cracked down on harshly, while the state of mind involved is one of absolute dehumanization of your victim.
Hate crime laws are a logical part of this--if you kill someone simply because of their race, that motive has to be taken into account during the trial. As a motive, (1) it provides no reasonable justification for your crime, (2) it carries an extremely high risk of re-offense, and (3) it has many of the same problems of assassination--dehumanization and risk of widespread recurrence in the form of racial violence. These factors, taken as motivations in the same line as the other motivations given above, are all reasons crack down on 'hate crimes' extremely harshly. In the legal hierarchy of motivations and states of mind--which have always been used to determine severity of punishment--racism and religious prosecution are among the most serious.
Finally, political correctness. I'll be brief here. Fundamentally, most of the 'political correctness' we see in our society has less to do with ideology than with market forces and globalization--people who want to sell to the greatest number of people possible, colleges who want to attract as many applicants as possible, jobs that want to be able to employ and sell to absolutely everyone. This leads to sometimes silly-sounding inoffensiveness.
Some time in the mid 80's to 90's, conservatives realized they could gain traction by blaming this on liberals, and to an extent it stuck... it's humorous and certainly worth making fun of in the game. But it isn't real; if you actually look at the words of liberal thinkers or the platforms of liberal political parties, you won't really find any more 'political correctness' there than you would find among conservatives (and less, in some ways--the conservatives have the 'moral majority' folks breathing down their necks, after all.) Liberals and conservatives each have jokes they tend to find tasteless or stupid; neither has a monopoly on sensitivity.
From a liberal perspective, conservative efforts to undo the separation of church and state and 'moral majority' efforts to censor culture are the most serious threats to free speech in the country today.
Privacy is much simpler. Much of modern US conservatism does not recognize an enumerated constitutional right to privacy. I am completely, 100% serious here; this primarily has to do with conservative rejection of Roe v. Wade and gay rights arguments, both of which are grounded in that concept. Rick Santorum, for instance, who was one of the most conservative US senators during his tenure and a vocal representative of his party's more conservative wing, once famously stated that the right to privacy "doesn't exist in my opinion in the United States Constitution". Most of the most pressing issues with regards to privacy (ignoring war-on-terror-Bush administration debates, which are ultimately transient and would certainly put liberals on the side of privacy if considered) have to do with sexual privacy, which liberals strongly support and conservatives reject utterly in concept.
...that went on a bit longer than I'd intended. Now, much of that is broad generalizations or whatever (many conservatives certainly support the right to privacy!) But the game is intended to be humorous, and paints in broad strokes to that effect... its conservatives are ultimately faceless corporate fundamentalists, while its liberals are fanatical free-everything hippies. The positions supported by the LCS accurately represent this comically simplified divide.
[ July 12, 2007: Message edited by: Aquillion ]
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