I'll preface by saying that I don't support the banning idea but I'm happy it's being suspected which is a chance for the community to decide.
I'll start by deconstructing what I think is the "best" copypaste swagplay team. Any parafusion team straying from this will be easier to beat.
Hazards: Deoxys-S, Deoxys-D, Smeargle
Absol/Espeon Counter + Sweeper: Greninja, Aegislash, Dragonite, Scizor, etc
Klefki
Thundurus-I
STAB Foul Play: Sableye or Liepard or Murkrow
Ditto
None of their pokemon hit particularly hard on their first turn in, not even the sweeper. There's only three things you'll need to do to get yourself in the winning position (easier said than done against a good opponent):
1. Control the hazards
2. Always be able to switch switch switch out infinitely between two pokemon that will never fall perish to Foul Play.
3. Have some checks against the meta to handle their sweeper
1.a. Nothing beats Deoxys-S except Magic Bounce, but that's a different discussion. Even a prankster-taunt lead will 50/50 against Magic Coat variants.
1.b. Some Hazard leads also run mental herb, preventing taunt
1.c. All is not lost, these pokemon are the best hazard leads but also die easily and can generally only do their job once
1.d. Every team, even HO, has room for Defog or Spin somewhere. Latios, Mew, and Excadrill are offensive examples, but note their weakness to Foul Play
1.e. Make hazards your first priority. A defogger or spinner immune to paralysis or with a lum berry will help you immensely
2.a. This is easy for defensive teams, manageable for balanced teams, and difficult for offensive teams.
2.b. You can only infinitely switch if hazards are down and you have something like leftovers or poison heal or reliable recovery
2.c. Defensive teams switch between: Alomomola, Tangrowth, Gastrodon, Blissey, Mandibuzz, Clefable, Sylveon, Florges, Umbreon, Tropius, Whimsicott, Togekiss
2.d. These pokemon can try to attack once and if they fail due to parafusion it doesn't matter, no damage taken, switch out to another teammate
2.e. Balanced teams have the above and: Chansey, Rotom-W, Hydreigon, Hippo, Azumarril, Chestnaught, Gliscor, Breloom, Cobalion, Ferrothorn, Skarmory, Zapdos
2.f. These pokemon are on a timer and take decent damage from Foul Play, but have many many tries due to their recovery, defenses, and typing
2.g. Offensive teams might try: Tornadus, Mienshao, Reuniculus, Conkeldurr, Scrafty, Krookodile, Salamence, Dragonite, Zygarde, Lati@s, Talonflame, Pinsir
2.h. Some of them have recovery, some of them have priority attacks best used on a free switch in, most of them really don't appreciate Foul Play though
3.a. A general purpose pokemon with priority faster than Klefki is a great start: Thundurus-I, MegaScizor, MegaMedicham, Talonflame
3.b. Consider a ground-type or electric type for the paralysis immunity
3.c. You could also give it a Lum Berry for confusion. Garchomp, Excadrill, Diggersby, Rhyperior, Landorus-I, Landorus-T, Raikou, Rotom-A
3.c. There are pokemon like Suicune, Quagsire, Flygon, Terrakion, Keldeo, Lucario that generally work well against swagplay but I didn't fit them in earlier
I hope everyone tries out a few new ideas against the swagplay strategy. I think it's very possible to prepare a team that does well against them, as well as being viable in the OU environment as a whole. It was Einstein who said that insanity is doing the same thing over and over again and expecting different results. Maybe certain types of teams will be very weak against parafusion but very strong against, say, baton pass teams. Look over your team and see if you can deal with swagger in the mean time, it's definitely popular on the suspect ladder.
And always remember that the low ratings area is full of experienced alts with skill far beyond their current rating so don't pull out your hair if you lose to the team archetype every now and then, you'll probably win the next 4 games against them. I think the OU suspect announcement and controversy that goes along with any smogon decision has added momentum to the fad and the teams might be more popular now than they were in the past, but from my experience they weren't overwhelmingly omniprescent on the ladder and because it's generally a poor strategy you'll probably win much more often than not if you put in effort towards countering it.
Here, "counter" has a meaning different than "be able to switch in and force it out". In this context it means having pokemon that swagplay users can't touch and PP stalling them while you heal up, gambling only with safe risk/reward opportunities, minimizing their ability to status you, and don't let the ditto sweep.