Of course they’re a threat to the “system”.
But if this is how you see the spread of political opinions:
There’s really nothing sensible you can say about politics.
Your entire system is designed to let you lump everybody who disagrees with you into a few groups you can hate. And, of course, by attributing “racism” or “Fascism” to large groups of people it doesn’t apply to, you give yourself an excuse to hate without actually thinking whether they deserve that hate.
By any definition of “Left vs. Right” that most people would accept, both your “Conservatism” and your “Libertarianism” occupy huge spreads, overlapping both “Moderate” and “Liberalism” (which also have large spreads).
It’s clear to anyone who actually thinks about it that more than a single dimension is needed to properly classify different political positions. For instance, Brendon Swedlow, in an article “Beyond liberal and conservative: Two-dimensional conceptions of ideology and the structure of political attitudes and values”, offers several different 2-dimensional scales using various measures. (I just found this example in a quick Google search, I’m not saying I agree with him, or have even read the whole article.)
Personally, I would suspect that you’d need a number of dimensions (5–10 at least) to properly map thinking people’s political/social/economic opinions.
Of course, it’s plausible that collectivists such as “communists” would find it hard to actually map political opinions in a way that considers individual opinions.
Certainly libertarians would be all over the map in most of Swedlow’s examples. (Well, not really, but they’d be much more spread out than the various maps suggest.)
I’ve interacted enough with conservatives to be pretty sure it’s the same for them.
“Liberal” has several different meanings in several venues, from something similar to “radical progressive” in the US to the sort of “classical liberalism” represented by Hayek. And that’s before you start considering the individual opinions of people who actually think about their politics.
People in all the groups have various powers such as votes, money, social networks, persuasive powers and platforms, etc. which can make them threats to the “system”. By working with them, you have the option of pointing people whom you fundamentally disagree with to persuasion on that topic that might be more effective than yours.
Rather than thinking of “movements”, perhaps it would be better to think in terms of special-purpose alliances, applying only to the specific agenda item in question, and accepting that on other items, there will remain differences.
I realize this might be hard to grasp for somebody immersed in collectivist mindset(s), but it’s really a better description of how politics really works. In fact, IMO one reason that “socialists” so frequently end up in bitterly feuding factions is that they apply collectivist expectations to anybody who allies with them for any purpose.