Are you sure? I'm pretty sure that at least in Melee, Yoshi's parry had the same type of invincibility that you get when you respawn: moves can hit you and the opponent goes into hitlag, but you don't hitlag or take damage or knockback.
You misunderstood what I said. Yoshi is still invincible in PM during his parry. The difference is that, in PM, if Yoshi is hit while invincible, the same attack can still hit Yoshi's shield after the invincibility runs out (if the attack lasts that long) and his shield comes up or it can hit Yoshi himself if he attempts to jump out of the parry to attempt to punish. The invincibility is there (and probably for the same duration) but it doesn't prevent the attack's hitbox from hitting Yoshi/Yoshi's shield once the invincibility ends. Hitboxes don't just go away once they hit something. They are flagged so the game knows that it can no longer hit that same something after it has already been hit. Ganon's fair hits Mario, it gets flagged so the game knows not to make it hit Mario again every frame after that until the attack's hitboxes end. Multi-hit attacks have refreshing hitboxes, so the flag goes away and the hitbox can hit the character again (actually I think it's technically just a different hitbox that replaces the other one). So normally, in Melee, hitting Yoshi while he's invincible (or anyone while they are invincible) flags the hitbox as having hit Yoshi, so the game knows not to register the hitbox as having hit Yoshi
again, even if it passes through him once he begins to jump even though he's vulnerable at that time. In PM, the invincibility doesn't do the same thing for Yoshi. It flags the hitbox to not hit Yoshi's invincibility again, but the flag doesn't apply to Yoshi's shield or Yoshi's normal, vulnerable hurtboxes, so it can hit those after hitting invincible Yoshi.
If I'm wrong somebody correct me