Looking that the three EG threads again this time for uses of "PUA" and "MRA". In this context "PUA" stands for "Pick-Up Artist" and "MRA" stands for "Mens Rights Advocate." My understanding is that PUAs are men who give or have taken lessons on how to "pick-up" women for sex or relationships. In contrast (again in my understanding) MRAs are people (not just men) who are concerned about equal rights issues for men, for example gender differences in work related fatalities or child custody in family court. While overlap between the PUAs and MRAs is possible, you wouldn't necessarily expect it (you might expect PUAs to be predominantly young single men, while you might expect MRAs to be older divorced men with children, a person can't fit both of those stereotypes at once), for that reason it is somewhat amusing that when used as epithets, the commenters use them almost synonymously as if they don't really understand the insults they're using.
Additionally, both PUAs and MRAs are very much "opt-in" in that if you don't know what they are, then you almost certainly aren't one (except by some very broad definitions of those terms), so the fact that many of those who received these insults had to look them up, means that the accusation was false. Given this, why do they use those terms as insults? Because to their thinking both "MRA" and "PUA" basically mean "misogynist." In their view PUAs treat women as objects, and are therefore misogynists, and MRAs fight against women politically, and are therefore misogynists, and this is assuming they make any distinction between those things at all (the fact that they think a PUA would write an "MRA manifesto" suggests that they don't). Make no mistake, if they call someone an MRA or a PUA, they are trying to insult and slander that person.
I'm not going to make a distinction here between saying someone is an MRA or PUA outright, and saying that they have MRA-like views. I understand that this is arguable, but saying someone is a misogynist and just saying that they are "parroting misogynistic thought" is too close for my comfort. Also the accusations will often be made about all those who disagree rather than a specific commenter, for example: "Aaaand the MRAs have arrived. Oh what FUN!"
Looking at the first thread "Always..." the term "PUA" appears 7 times and it is insinuated that someone is a PUA twice: by Rev. BigDumbChimp at #188 and again at #231. "MRA" appears 34 times and is used as an epithet 25 times in total. Those who used it: Amphigorey (#379), Brother Ogvorbis (#438), plien (#478), Ing (#719), RahXephon (#724), Caine (#735), Bryant Belknap (#752), Caine (#762), Brother Ogvorbis (#788), Brother Ogvorbis (#869), Josh (#878), JustALurker (#901), ted (#968), Caine (#1040), Josh (#1059), Caine (#1092), Caine (#1107), Caine (#1118), Andyo (#1131), Caine (#1134), Caine (#1140), Caine (#1173), Some bloke or another (#1196), tielserrath (#1216), and Brother Ogvorbis (#1276).
Looking at the second thread "Decent..." the term "PUA" appears 8 times and is discussed in thread but not used as an epithet explicitly. "MRA" appears 44 times and is used as an epithet 18 times. Those who used it: Philip Legge (#36), Carlie (#62), Caine (#82), oihorse (#103), Ms. Daisy Cutter (#142), Andyo (#201), Rey Fox (#211), strange gods before me (#282), Andyo (#418), Cerberus (#498), Nerd of Redhead (#514), Nerd of Redhead (#533), Algernon (#541), Matt "Nora" Penfold (#598), Josh (#629), Caine (#633), Daredevil Dan (#646), a_ray_in_dilbert_space (#704).
Looking at the third thread "Oh no..." the term "PUA" appears 5 times and is used as an epithet 3 times total. Those who used it: webriggs (#177), Carlie (#777), and mouthyb (#852). "MRA" appears 69 times and is used as an epithet 30 time total. Those who used it: Gyeong Hwa (#54), Caine (#127), Caine (#140), Caine (#185), RemembersABeach (#199), Nerd of Redhead (#214), Jessa (#235), Harmless Eccentric (#254), Daredevil Dan (#306), plien (#310), Andyo (#325), Brother Ogvorbis (#334), Andyo (#431), Shala (#448), plien (#464), Aratina Cage (#517), Caine (#551), Philip Legge (#590), Caine (#604), jcmccreight (#629), Philip Legge (#641), Carlie (#777), Algernon (#805), Algernon (#828), John Morales (#831), Andyo (#855), makyui (#857), Andy (#863), Algernon (#873), and Andyo (#878).
So that's 5 uses of PUA, and 73 uses of MRA over all three threads.