What is the test that determines doctrine from discipline? Some of the hubbub around the Synod on the Family in 2015 has been (at least superficially) around whether disallowing civilly remarried couples, without annulled marriages, whose original spouses are still alive from communion is a doctrine (and therefore unchangeable) or a discipline (and potentially malleable) so what makes this part of marriage  doctrine.  Are there other rules concerning marriage that are discipline and not doctrine? Is it possible to have invincible ignorance when it comes to receiving communion in an invalid marriage?
Dogmas are truths proclaimed either directly by God or by God through His Church. That one cannot and should not receive Communion in the state of mortal sin is not a changeable discipline but a dogma of the highest degree, de fide.

The 24th Session of the Council of Trent says:


  Canon VII.—If any one saith, that the Church has erred, in that she hath taught, and doth teach, in accordance with the evangelical and apostolical doctrine, that the bond of matrimony can not be dissolved on account of the adultery of one of the married parties; and that both, or even the innocent one who gave not occasion to the adultery, can not contract another marriage during the lifetime of the other; and, that he is guilty of adultery, who, having put away the adulteress, shall take another wife, as also she, who, having put away the adulterer, shall take another husband: let him be anathema. 


Now,


adultery is a mortal sin (cf. Matt. 19:9).
Divorcing and remarrying is adultery.
Therefore, divorcing and remarrying is a mortal sin.


He who receives Communion in the state of mortal sin, i.e. "unworthily…shall be guilty of the body and of the blood of our Lord. … [He] eateth and drinketh judgment to himself, not discerning the body of our Lord." (1 Cor. 11:27,29).

Living in sin also causes more sins: scandal, temptation to other spouse to commit adultery, and a grave injustice to the children.