I think you're reading CA wrong.
What that implies is that the unit's benefits from skills that give it a weapon advantage are negated, not the normal weapon triangle. Thus, if the unit has TA or a gem weapon, they no longer get any benefit from those.
On the other side of things, if your opponent has TA or a gem weapon, then the benefits from those are now reversed but only if the weapon triangle was not in your favor to begin with.
So, for example, Reinhardt with CA is attacking a Titania with Emerald Axe+. While normally the Reinhardt would do -20% damage from weapon triangle and another -20% due to Emerald Axe+, with CA, he would be at 0% disadvantage, CA flips the -20% due to Emerald Axe+ to +20%, negating the -20% due to weapon triangle.
I don't think it changes Rein's matchups too much though. Most of what Rein is running into, in terms of counters, aren't running TA or gem weapons, they're running fury, like Julia or Nino. I'm more curious as to how it changes B!Cordelia's matchups. I need to run the numbers on that, unless Roman has them on hand? Can't check it specifically till later on. Swordbreaker vs. CA.