I like to first judge a piece of art all by itself and think about it for a while. 
If it really intrigues me or makes me think then I'll go back later to check the artist out if I don't know them already.
I've never felt that knowing an artist's bio has tainted the work for me.  So far, familiarizing myself with an artist has only made their work deeper and richer for me.
I like knowing precisely what a piece of work springs from and I'm still free to recognize the truth the work holds for me.
I don't know if there's any 'should' to it.

Thanks, Linda -- you put it so eloquently that I am inclined to agree with you. But still, I think not all people would react the same way. For many people, art is opaque, and psychology represents a way "in" which does not actually do justice to the work. It becomes a way of feeling that one "knows" what's going on without actually having to encounter what is being said.

In my experience, most of the time psychologizing is used to flatten art rather than give it depth. Maybe what's important in the approach you're describing is that you encounter the work of art on its own terms, first?

I don't know, Penelope Rose.

I don't know if we can ever see art in its own terms.  The minute anyone casts an eye on it there are two things involved: the art and the eye, and those two things conspire to make something unique in the mind of the person observing, and then there's the artist who makes the third entity if the observer cares to consider that poor forgotten workhorse.

I'm appalled that anyone considers art to be opaque--although that's certainly a valid way of looking at it at first but after you've seen it as the thing in itself it morphs into what you think it is or what you feel it is or what you hope it might be.

I love to know what an artist was trying to get out of himself and I love to know what other critics think of a work of art but it doesn't touch what I feel about it myself, although what I feel about it usually changes as time goes by and more life happens to me.  At each stage of my life I would have seen and felt something different about Judith's murderous demonstration.  Had I been raped by a person I trusted--well, that would change my observation of it altogether.

All art for me is a lens.  The artist creates through the lens of talent and desire; the observer sees through the lens of experience and no two people ever create or observe the same thing whether on canvas or in the mind.  Your very question has added a new layer of complexity for me.

I'm probably misunderstanding your question completely and I apologize.  I didn't know about the opaque business and it lighted a fuse.  I'll be quiet now.