Listening to digital and analog

I find it so interesting that many people prefer listening to distortion. The vast majority of recordings done since the mid 80s are digital. If a digital recording sounds different at all when played back through an analog system, that difference is by definition "distortion." In digital form music is just data, binary numbers, distinct values. As long as the data is not corrupted there is no distortion, none all the way to the final DAC and the first analog step. Remember analog cell phones? pretty bad. Now we have digital phones, clear as a bell regardless of how crappy the signal is until you lose it entirely. 
So, many prefer playing a record made from a digital master to just playing the digital data back through a DAC. Forgetting about background noise and issues generic to vinyl playback but you also add distortion produced by the cartridge and phono stage added to the mix. 
There is absolutely nothing wrong with good digital playback. It is eons superior to analog playback. It is just that some brains can't get a handle on it. Proof that you hear what you think you will here. Lay instinct. 
I think it is amazing how good vinyl playback can get. I certainly have records that sound better than their digital counterparts. But, that difference is a mastering issue and not the fault of digital playback. The best playback I have ever heard was from high resolution copies of digitally recorded music. 

"On the contrary, I must adapt a different way of listening that doesn’t actively compare the two.  If one keeps the analog ideal always in mind, it makes it difficult to appreciate digital music."

It's hard to make out your premise and your argument.  How about this:  If one keeps the in-person musical experience ideal in mind, it makes it difficult to appreciate recorded music.  This would seem even more difficult but we are all here because we do appreciate recorded music.  And IMO it's not difficult at all!

"I just want to point out that you may have to listen a little differently to each in order to enjoy both"

Actually, how does one listen differently?  Can't figure that out.  As for me, I just sit down and . . . listen.

I thought someone would question me on how one listens differently.   (I’m surprised no one has brought this up til now.)
And your point about the in-person experience vs. the recorded experience is also pertinent.
I do believe one has to listen differently to recorded music, to “suspend disbelief” in order enjoy recordings, which seldom if ever match the real thing. Same with digital vs. analog.  I think digital is less “real” than analog.
You may disagree.

@yeti42: 

"To me, analog is more textured and real sounding, (some, or many  may not agree)  but does that mean it’s not possible to enjoy digital sound?  On the contrary, I must adapt a different way of listening that doesn’t actively compare the two.  If one keeps the analog ideal always in mind, it makes it difficult to appreciate digital music. Therefore I have to block that ideal from my mind and listen to digital on its own terms. It must generate its own reality.  Only then, can I sit back and enjoy."

This thread makes me grateful that I don't have this problem!   

You’re lucky!