Now let us say you are in a position of influence over the state to take over this system and reform it.

You've basically just stated why I'm unconvinced by your argument.

The church had massive authority in the middle ages. They could have very easily ended the practice of criminalizing religious dissent. Even if you think that was impossible (and there's no reason why it should be) it would have been an even simpler matter to just quit killing people for it. People probably wouldn't even be talking about this now if all the church did was slap a fine on them or lash them or something.

Can you reasonably conclude that the church stepped in to install due process? Yes, that appears to be the mainstream view of it from what I can tell. But can you reasonable conclude that the church was some kind of unwilling participant in the murder of accused heretics? Absolutely not.

Are you saying the Christian thing to do is not get involved and let the innocent get slaughtered so you can sit back and claim your hands are clean?

The innocence-guilt dichotomy here continues to be a problem, so I'll repeat my point that I respectfully think you missed: there's no moral difference between killing a Catholic and killing a religious dissident. The church wasn't saving innocents. They were actively participating in their judicial slaughter. Saving innocents would be if they had a policy of never ruling anyone to be a heretic. Murdering innocents is finding a person guilty of the non-crime of disagreeing with you when you know full well that your decision is a proximate cause of their death.

You seem to be really trying hard to condemn the Church when you should be grateful they got involved. The Church saved thousands of lives and you think what the Church did was evil.

Yes. I think murdering people for their religious views is wrong and the fact that so many Catholics seem unwilling to agree with that is a huge part of why I stopped considering the Church as a valid option a long time ago.