The line I am drawing is conceptual. And is important.
Religion and politics are different human endeavors. While this innate human desire to control everything and everyone around us to our own advantage crosses all conceptual boundaries and infects all our human civil and cultural endeavors. This obsessive desire to control is NOT PROPER RELIGION. And is NOT PROPER POLITICS, either. It's our self-centered fear infecting our efforts in these other areas of civil discourse. So if you want to address that selfish fear, then fine. But stop blaming it on the various human endeavors that it infects, like religion or politics (and commerce, etc.). Because they are not the cause. They are the victims. We humans NEED religion and politics within our social systems. So we NEED to somehow rid them of this fear-driven obsession with control.
That's where our efforts ought to be. Not in blaming and trying to destroy religion and politics.
Let's start with the last point first. I'm neither trying to destroy politics nor religion.
Where humans band together in some sort of consolidated and consistent fashion, we are faced with both a band of individuals, each with their own thoughts, desires and actions, and a group, with stated goals, policies, dogma and/or plans.
We can assess, criticize, assist or otherwise note the individuals, and their behaviours.
But so too can we assess, criticize, assist or otherwise note the behaviours of the group.
It is entirely valid (for example) to criticize the Australian government for certain actions, or laud them for others. So too, the Catholic Church. So too the GOP. So too the Australian Cricket Team, for that matter.
In no way does that suggest a need to destroy governments, religion, opposition parties or sports teams. But your argument about 'proper religion's and 'proper politics' is a goal without a path. Nor one with a history.
Politics is about control, whatever it 'should' be. At it's best, it's been a way to share and cede control, but it is literally the means by which the decision making process of a shire, state, country or organisational body is determined.
And religion (beyond mere spirituality and belief) is about dogma, convention and standards. I can certainly envisage (and maybe even point to) religions that don't try to control anyone (be they members or non-members). But through a mixture of scriptural assertions, cultural standards and outright power, that is most often not the case.
So...do I have a problem with religion? Nup. You can choose whether to believe that or not, but I have no issue with religion. Do I have an issue with politics? No. I'm not sure what it would mean to, since I can't think of a human society without it.
Do I have an issue with certain coherent groups beneath those umbrella terms? Sure. In some cases certain decisions and positions, sometimes more holistically. But so do you. So...colour me confused.