No, you don't forfeit the right to self-defense if you're illegally possessing a firearm.
At least, it's not that cut and dry. On top of that, for the love of Jeff, RITTENHOUSE WASN'T IN ILLEGAL POSSESSION OF A FIREARM. The charge was thrown out. Also, there's a difference between owning a gun and possessing one. No, Rittenhouse couldn't own the gun legally and he didn't own the gun. He could legally possess the gun.
But even if the charge weren't thrown out, there have been plenty of cases in which a person used a gun which he or she illegally possessed in self-defense and, yes, they faced charges for the firearm; but, no, they didn't lose their right to claim self-defense.
Moreover, do you really want the law to say that?
Gaige Grosskreutz wasn't allowed to be carrying the gun the way he was. He could own the gun and he could open carry; but, he wasn't allowed to conceal carry because his permit was voided due to prior weapons charges. If Grosskreutz had shot Rittenhouse and killed him, would you be reaching for a conviction of Grosskreutz due to his illegal carrying of a firearm? Would you be saying that Grosskreutz forfeited his right to claim self-defense by illegally concealing his gun? I think not.
There's also a horrible case that I would like to point out in Susanna Hupp, who was legitimately at the mercy of an active shooter and watched both of her parents murdered by the shooter. Hupp legally owned a gun but a law in Texas at the time made it a felony to carry her gun into the venue that ended up being shot up. So, Hupp left the gun in her car. If she had carried the gun into the venue and used it to shoot the maniac who killed more than twenty people including her parents, she would have done so with a gun that she was carrying illegally.
Are you honestly going to tell me that your ideal view of the law would be that, if Hupp dared to break that gun law and used the gun in that situation and Hupp should have lost her right to claim self-defense? Are you actually trying to say that, on top of any weapons charge she may have faced, she should also have faced murder charges because she was breaking a law by having the gun on her?
Well, she followed the law and a lot of people died because of that choice. If you believe that the law should be that Hupp should be facing murder charges for breaking that gun law, with due respect, no respect is due to you.