Christohypocrites assumes they're real Christians who fail to apply their beliefs to themselves but apply it to others. Christopretenders do not even preach real Christian beliefs to others much less follow those beliefs themselves. Why? Because Jesus is, was and always will be a socialist.
Using Christohypocrite(s) has drawbacks compared to the christopretens-/christopretend system:
Also Hypocrite just means says one thing, does another. It doesnt specifically encode insincere Christian identity for social and political advantage, propaganda to advance an often capitalist agenda and control others, commercial branding for profit, or to satisfy an insecurity without improving morality.
It's more insult than concept-handle: It functions mainly as a moral jab, not an analytical term you can extend into a clean word family.(adj./verb/system).
Weaker diagnostic value: It doesnt tell you that false Christianity exists, so its less useful for careful critique when those who are getting wealthy and politically powerful are using religion as an opium to feed the masses so they don't rebel against their exploitation like Karl Marx once said except he didn't distinguish between authentic religious beliefs like Christianity and religion being corrupted to be used by the powerful for their wicked ends.
It is not a precise, scalable concept term but it can be useful in judging moral shortcomings from Christian who truly do appear to believe what they claim to believe and are not in it for money or political power but they still violate Christian standards while applying those standards to others.