The major point of contention between Luther and Catholics is he believe in faith alone, while we believe in faith + doing things right.
So his having to protest, correct, splitting off, just goes to show how he self-refutes his own principles.
If faith alone is all that is required VOID of having to do things right which is what we insist you have to do, then why complain about Catholics doing anything wrong? It only proves us right, since we insist its not faith alone but you have to do things right.
A genuine true believer of faith alone would prove himself right by faith alone, not by requiring action taken like leaving to start his own church and then complaining that folks are doing things wrong.
So what if they do things wrong? Our biggest difference is you insist on faith alone and that you don't have to do things right.
In that respect we have similar beliefs but in our interpretation of scripture, good works are an outcome of faith.
Ephesians 2
8 For by grace are ye saved through faith; and that not of yourselves: it is the gift of God:
9 Not of works, lest any man should boast.
10 For we are his workmanship, created in Christ Jesus
unto good works, which God hath before ordained that we should walk in them.
If we do bad things we also have a similar belief - confession of sin. We believe acknowledgement of sin can be done directly to God.
1 John 1:9 If we confess our sins, he is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness.
Starting a new church: Well, honestly looking out over the vast expanse of Christendom we (non-Catholics) do appear to many as if we are sheep without a shepherd. Look at it this way, if the RCC is the True Church they have not done a good job listening to their "protests" - some yes but many abuses still seem to us to be falling on deaf ears.
e.g. (just one example): Statues in the churches seem as idols which are worshiped.
Although A couple of years ago I was really surprised. I went to a funeral mass of a close friend and there were no statues in this church, the mass was in English, there was responsive scripture readings and there were altar girls!
The altar girls were the biggest surprise!
HankD