It is literally exactly what conservative means. There is no other coherent definition of conservative. Conservative means valuing tradition and the preservation of tradition more highly than other aspects of governance. And there's no difference between your "entrenchment" and my "tradition'. Both mean the same thing -- 'we've always done it this way and so don't want to change'.
If someone's highest values are around and improvement of efficacy and efficiency of their government body, they would identify themselves as a progressive. If the values were protecting individual liberties, they would identify themselves as a liberal. If their values were to promote the fairest and most equitable society, they'd identify as socialist.
People can be many things at once. Most reasonable people are. But the word conservative still has meaning and the meaning is to cleave to tradition and traditional hierarchies. It's what the word means.
I would find it incredibly difficult to defend any organizations that refuse to change practice in light of evidence. I tend to be very progressive-minded and mostly not at all conservative, so I do not think tradition is a very good reason to refuse to change practice.