Particularly, what is his view on liberalism? And what is the significance of the example he gives regarding Catholics?
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Briefly, it seems that he thinks liberalism, ideally, is when a person in power takes the interests of a person without power so perfectly that his own interests get overlooked from time to time. He acknowledges the tension between this ideal and mere "sectarian" politics, and provides a path to elevating actual liberalism toward ideal liberalism.
He finishes with a restatement of the impossibility of ideal liberalism, since everybody has at least his or her own perspective.
Regarding Catholics who wish to be liberals, he points out the inherent conflict between belief in a particular religion of the kind that admits salvation for anybody and ideal liberalism, which does not admit such partisanship.
One argument Nagel makes is that as with Occam's Razor, government policy should be set by the framework that requires the fewest positive assertions, and that this is a good way to resolve conflicts between ideologies.
On page 233, Nagel asserts that the morality of abortion is unfalsifiable since no objective account can be made without positive assertions. Therefore, Nagel says that it is best if government refrain from regulating abortion, even though this position "has the same effect as we would get if the law were based on the positive position that whatever people choose to do in these areas is permissible."
But analyzing abortion's morality is less complicated than Nagel thinks. For abortion to be permissible requires the positive position that "an unwanted fetus is not a person". This position is more positive than supposing that "all persons are alike, regardless of their condition."
Most arguments for liberal abortion regulation include the assertion that "an unwanted fetus is not a person", and policy would by-and-large be made differently if those arguments were vacated.
Simon Caney, who does not accept the validity of Nagel's arguments in 'Moral Conflict and Political Legitimacy', none the less provides an accurate overview of its central contentions :
THOMAS NAGEL argues that the state should be neutral between different conceptions of the good life. He thus commits himself to what has been called justificatory neutrality - the view that the state should not make policy on the basis that some forms of life are superior to others. ...
Nagel is impressed by the phenomenon of reasonable disagreement between people over the nature of the good life. He argues that the state should 'not impose arrangements, institutions, or requirements on other people on grounds that they could reason- ably reject' (p. 306), and that because reasonable people disagree about the good life, therefore, the state should desist from promoting valuable forms of life.
Stated more formally Nagel argues as follows:
(P1) a principle P is a legitimate political principle only if
(1) it is 'possible to present to others the basis of your own beliefs [P], so that once you have done so, they have what you have, and can arrive at a judgment on the same basis'. (p. 315)
(2) one can provide a non-circular explanation as to why some people reject P (p. 316)
Nagel then argues (P2) that reasonable people disagree about which conceptions of the good are valuable and how one establishes which are most worthwhile. In fact the disagreement is so radical that it is impossible to justify the superiority of some ways of life to all reasonable people. Hence he concludes, (C), that a state that promotes some conceptions of the good is illegitimate since it cannot satisfy the criteria specified in (P1): it would be acting according to principles which some reasonable people reject. Therefore, the state should be neutral. (Caney: 41.)
Jusificatory neutrality, as explained above, is Nagel's version of liberalism.
Nagel assumes that instability ensues when citizens believe that the state makes policy on the basis of reasons which they reject. Thus he assumes that the state will cause instability when it does not satisfy justificatory neutrality. But, individuals may also feel aggrieved even if the state has observed justificatory neutrality, but when as a result their form of life has suffered. Catholics, for example, may be resentful of a state that is neutral because the consequences of this justificatory neutrality are that Catholicism suffers. That is individuals might be concerned more with the consequences of state policy than with the reasons underlying state action. Indeed, as Nagel notes, many non-liberals think that neutrality is a 'sham, and that all the pleas for toleration and restraint really disguise a campaign to put the state behind a secular, individualistic, and libertine morality' (p. 301). If this is true then a Nagelian impartial state will not necessarily secure the stability Nagel proffers. Thus Nagel's defence of his claim that the state can only adopt those principles which all reasonable people accept is unpersuasive. (Caney, 44-5.)
The major point here appears to be that while it may well be the case that the state is unstable when it does not observe justificatory neutrality, it may also be unstable when it does - as when such neutrality is harmful to the interests of a group. Catholics are taken as an example.
Thomas Nagel, 'Moral Conflict and Political Legitimacy', in Authority edited by Joseph Raz (Oxford: Blackwell: 1990).
Simon Caney, 'Thomas Nagel's Defence of Liberal Neutrality', Analysis, Vol. 52, No. 1 (Jan., 1992), pp. 41-45.