You think wrong.
The 14th Amendment EPQ specifically reads:
"nor shall any state deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws."
What legal process are we discussing here? That cops aren't immediately arrested and charged after an on-duty shooting and the a citizen who killed someone would be?
Well, the constitution provides that no person can be arrested without probable cause that a specific crime was committed (or a warrant signed by a neutral magistrate that also contains probable cause). If there is probable cause the officer broke the law in the shooting, he would be arrested and required to post bail, just like anyone else. If the shooting is simply under investigation, even if it seems suspicious, there's not probable cause, and, just like everyone else, the cop isn't arrested or charged. Cops are guaranteed almost the same due process protections as you and I, although Garrity v. New Jersey carves out some variation in specific circumstances.
The 14th amendment guarantees equality of process, not equality of outcomes. If there were a law on the books somewhere that said "any cop charged with a crime is granted release on recognizance" or "cops can't be arrested for crimes", there would be a great 14th amendment challenge to that law. I do, however, generally agree with your argument, I'm just a miserable pedant.
You are given benefit of the doubt by becoming a police officer only and not by running a charity or doing ministerial work or working with underprivileged kids or being a doctor at a non-profit or any of the multitude of other things you can do in life that would warrant being given the benefit of the doubt?
You're guaranteed the benefit of the doubt regardless if you are a thrice convicted child rapist or Mother Teresa. On bail and bond considerations, all those things you listed are great examples of ties to the community and a reason to be released on a considerably lower bond.