The Moderate Liberal tradition is liberalism grown up. It is not the triumphant, world-remaking liberalism of the nineteenth century, sure that reason and progress would perfect the human condition, but the chastened, sober version that absorbed the catastrophes of the twentieth and kept its nerve anyway. You believe that constitutional democracy, when it functions, produces steady improvement — that both markets and regulation have their place, that society should evolve thoughtfully rather than convulse, and that neither revolutionary ambition nor ideological purity is necessary when institutions allow measured reform in response to evidence. Yours is a liberalism humble about its ultimate ends and firm about its immediate enemies, and it regards that combination not as a failure of conviction but as the beginning of wisdom.
The realist foundation is Walter Lippmann, who spent a career thinking honestly about the gap between democracy's ideals and its practice. In Public Opinion, Lippmann punctured the comforting fiction of the omnicompetent citizen — showing how much of what we "know" about public affairs is secondhand, simplified, and shaped by the "pictures in our heads" — and the later Lippmann turned toward a defense of constitutional liberalism and the "public philosophy" he believed a democracy needs to steady itself against its own passions. From him your worldview takes its realism about what self-government actually requires, and its refusal to mistake democratic sentiment for democratic competence.
Judith Shklar gave the tradition its deepest and most honest reframing: the "liberalism of fear." Liberalism, on Shklar's account, is best justified not by some positive vision of the good life or human perfection — visions that have a way of curdling into coercion — but by the avoidance of the summum malum, the worst thing, which she named without hesitation as cruelty. "Putting cruelty first" means building institutions whose primary job is to prevent the abuse of power, the torture, the terror, the tyranny that are the constant temptations of politics. It is a liberalism modest about heaven and ferocious about hell, and it asks of any arrangement first not "does it perfect us?" but "does it protect us from the worst we can do to each other?"
Michael Walzer kept the tradition rooted and plural. Against a liberalism of abstract universal principles deduced from first philosophy, Walzer argued in Spheres of Justice that justice is the defense of different distributive logics in different domains — that money should not buy what belongs to love, or to citizenship, or to office — and that the standards we should hold a society to are the ones embedded in its own shared understandings, brought to light by what he called "connected criticism." From Walzer your liberalism gains its sense that reform works best when it speaks a community's own moral language rather than lecturing it in the universal.
Amy Gutmann supplied the account of how a divided society governs itself decently. In a world of deep and permanent disagreement, Gutmann argued, legitimate politics proceeds through deliberation — the give and take of reasons among people who respect one another enough to keep arguing rather than to coerce or secede — and democratic institutions are at their best when they cultivate that reciprocity. And Richard Rorty gave the whole tradition its philosophical permission slip. Liberal democracy, Rorty insisted, does not need a foundation in human nature or metaphysical truth to be worth defending; we can be humble about whether our values are grounded in the structure of reality and fierce in our commitment to them anyway. We do not need a theory to know that cruelty is bad and solidarity is good — and a liberalism that stops demanding certainty before it acts is a liberalism that can actually live in the world.
What you inherit, then, is a liberalism that has traded utopia for the avoidance of catastrophe, and certainty for institutions — and that believes this trade is maturity, not surrender. From Lippmann, the realism about the public and the need for a steadying public philosophy. From Shklar, the liberalism of fear that puts cruelty first. From Walzer, justice rooted in a society's own shared understandings. From Gutmann, the deliberation that lets a divided people govern itself. From Rorty, the humble, post-foundational defense that can commit without certainty. The throughline is that constitutional democracy is a self-correcting machine for measured improvement — not a vehicle for the perfect society, but the best instrument yet devised for preventing the worst one and inching toward better — and that its defenders should be modest about their ends and unyielding about cruelty and tyranny. The tension you carry is the one every era throws at the center: that moderation looks, from the outside, like timidity — a managerial defense of a status quo that serves the comfortable, an unwillingness to dream that cannot inspire the way the extremes do. In polarized times the vital center is squeezed from both sides, and a liberalism that has given up grand visions can struggle to give people the meaning and belonging that ideologies hand out for free. But you hold the politics that, wherever it has actually governed, has produced the freest and least cruel societies human beings have ever managed to build — and you suspect, with some evidence, that the dreamers who promise more usually deliver less, and sometimes deliver the very horrors your modest liberalism exists to prevent.