How do you manage your professional integrity when policies or administrative decisions conflict with best practice guidelines?

This is an eternal conflict. Once an organizational polices/decisions are signed they get old and stale. "We have always done it this way." is always the phrase you hear. This was even said when hospital decided it was time to stop allowing smoking, when I tried to open the visiting hours to meet the AACN research, when the emergency preparedness requirement for Y2K (yes I am old enough to have been the coordinator) were developed.
"The only one who likes change is a wet baby" is a frequently heard phrase when doing quality improvement processing.

If the policy does not violate any law, regardless of how dated, or out of the current mainstream belief, AND is not actually causing harm to the patient, it is time consuming to get things changed. Every change has to have its champion.

The champion usually gets a lot of pushback for wanting to change anything despite those doing the pushback being fully aware the idea has high merit.
Sometimes allies can be found among the staff, or the insurance companies decide they will not longer pay for the old way ( then change is done at light speed).
Sometimes if a 'powerful doctor - read high volume high profit admitted - wants something updated it will happen quickly. If they don't want to change it won't happen.

IF you believe the change is needed you need to be the champion, create a QI report/project/ and gather all your research and information, It always helps if you have a cost analysis to show the hospital can save money and improve patient care by tossing out the old and brining in the new. If the cost is more and the outcomes are minimal different it is unlike to change.

Finally if you cannot make the cage you want you need to move to a new department or workplace.