I find it a bit difficult to understand the bottom line of your question, because I feel there are multiple issues being conflated here. I will concentrate on this:
There are many users who recognize the problems with the new CoC [...] and there are their enemies. They seem to be organized in flag brigades and use moderators as a tool for their own sake by rising rude flag.
A quick clarification before I go on: the messages you linked to contain comment links. If a comment gets deleted, clicking the link will take you to the question or answer where the comment was posted. So if you find such a link and it leads to an answer that should not be deleted: well yeah, the original comment is now gone!
Whether or not the new (only slightly altered) CoC is helpful or not for the LGBTQ+ community is a debate on its own. Cis and trans people even disagree amongs themselves and I don't intend to discuss that here.
What seems to be a larger issue is the interpretation and planned enforcement of the updated CoC, which is in great part shadowed by the fact that it was heralded by the very unfair treatment of a user of a community in high standing (again, there's a lot to be said about this, and most of it has been said elsewhere).
However, the greatest issue is that the debate around the updated CoC and its official FAQ has sprouted an immense community response; and a lot of it not Nice. There's a wide gray area where we can argue that certain views fit into a person's personal beliefs, but there are a lot of examples of flat-out abuse (mostly transphobic, but also homophobic remarks). The worst of these don't live long on the site, because they are deleted fast, as they should be.
So how do abusive posts and comments get deleted? By flagging. Flagging is a key component in community-driven moderation. But the way flags are implemented suggests that it's very hard to do harm. You need several flags to destroy posts, and the full flag history is transparently visible to moderators and staff, complete with the name and date of the flaggers. One can easily imagine a band of trolls getting together to delete things with flags, but if anything gets deleted without merit, a single custom moderator flag can initiate an investigation on the matter, and I assure you that mods and staff will not take such flag abuse lightly.
So about the "flag brigades". Since you said you've only registered you might not be aware of moderation in chat. Some language- and moderation-related chatrooms support cv-pls tags (mild abuse of the tag markdown syntax in chat) to raise awareness of things to close. The tag itself reads as "CV please" for "close vote please", but everyone understands those to mean that this is only a request for other users to make educated, conscious assessments of the post being linked. It usually takes 5 pairs of eyes to have something closed in this manner.
Although we're talking about flag "requests" now, the dynamics is the same. You might see in the transcript that certain users are angrily asking for flags regarding the pronoun debate, and perhaps it's understandable to be angry considering the amount of filth being thrown around. My point, however, is that such a request for a flag doesn't imply that "a brigade" will jump on the post and flag it. Unless you think that everyone in chat is a mindless droid (I hope not!) you should see that these messages only raise awareness to content that the poster found unacceptable. What happens after is up to the discretion of every other user. They attach their names to their flags, and if something gets deleted when it shouldn't have, there will be repercussions.
If you see something get deleted when it didn't deserve it: raise a custom moderator flag and let moderators or staff investigate. Otherwise read between the lines, and notice that plenty of the flag requests are subsequently debated, and people will disagree whether something that was linked really deserves deletion. People's backgrounds and assessment of subjective issues varies, which is why several people have to agree for rude flags to do anything without moderator intervention.
But from the sheer volume of blatant hate that I've seen posted since the CoC FAQ came out (and summarily deleted), I urge you not to think that the lukewarm responses left alive on the site are representative of the posts that are asked to be flagged.