I'm curious what false doctrines you think there are. This is perhaps not a good place. Shall we try General Theology?
No need ...both believe Messiah came in the flesh, both believe Messiah is King, and Head of the Church, both believe that Messiah was in the Beginning of creation, and both believe Messiah is a God. It is these issues that our faith, and the Gospel only requires.
There is no mandate to worship the Son, but only that we honor The Son as a King and High Priest , and that we together worship The Father.
The dispute really is just a matter of revelation ...and to say who is lacking such a revelation, or who is above his brother for such a revelation should only be nothing more than discussion. No such divisions should occur, and no harsh treatment is warranted at all.
Now what is against The Law of the Assembly of our Messiah, is to murder our brethren, or to show partiality, or to call one a fool, or impose harsh torments upon one another, and to not stir up unnecessary schism ...We are commanded to love one another, and to forgive the faults of anyone who repents as transgressers of YHVH's Law, and the Word of our King, The King of Israel.
For this reason I too believe (over look my personal bias) that Arius suffered a supernatural death, or if one of Athanasius' succeeded in poisoning him AFTER Arius won the majority of the council's, and walking in triumph ...it can be said it was because his doctrine was correct, but his anathematizing of those who did not agree was a sin that YHVH could not leave unchecked. Because Arius too allowed what Alexander of Alexandria did to him, to be done to others who did not agree with Arius.
All in all, The ruler of this world subdued the Church because of this and created a counterfeit filled with all kinds of lascivious heresies, and blatant idolatries.
We need to love each other ...we are brethren, and that is what is important.