There are a couple points worth teasing out here.
First, on the issue of capitalization:
You don't capitalize words based on whether they're a noun or adjective. You capitalize them based on whether or not they're a proper noun (or derived from one).
Thus "libertarian" should always be lower case, whether as an adjective or a noun, when describing the ideology ("libertarians believe in basic libertarian principles like..."), while it should always be capitalized, whether as an adjective or a noun, when it's referring to the political party ("the Libertarian candidate running for the Libertarian party is...")
Jewish is always derived from a proper noun, so Jewish and related words should always be upper case, whether as an adjective or a noun ("That Jewish Jew is Jewish").
Feminism is not a proper noun, so whether we're using the term as an adjective or a noun is should be lower case: "the feminists support feminism." Even specific philosophies, like poststructuralist feminism or second-wave feminism aren't proper nouns, so they don't ever get capitalized, whether they are used as nouns or adjectives.
Second is the issue of egalitarianism "as a thing." I've never said that egalitarianism cannot be articulated as a thing encompassing a total philosophy. If you look at the sidebar of the sub you linked to, you'll notice that they make this point, too:
Egalitarianism (from French égal, meaning "equal") is a belief of thought that favors equality of some sort.
(my emphasis)
So even in /r/egalitarian, there is an acknowledgement that there isn't a single conception of what kinds of equality egalitarianism endorses. Even if we were able to demonstrate that everyone in /r/egalitarianism subscribes to one (total) philosophy, that still wouldn't erase the fact that there are deeply established traditions of egalitarianism as a total philosophy that mean other things.
That is to say that, even when we just focus on egalitarianism as a total philosophy, there is more than one meaning of the term in circulation. Even as a total philosophy, egalitarianism signals a commitment to some sort of equality, but doesn't specify what sort(s) of equality count as just and what sort(s) of inequality are acceptable.