Ever since Labrys first published the English version of their book, Hellenic Polytheism Household Worship in 2014, there has been something of a controversy in the English speaking Hellenic communities over the use of pictures on shrines. The book unequivocally states that statues must be used on shrines and that pictures are prohibited. I would give you an exact quote, but I gave away my copy of the book when I moved to China. If anyone has a copy and wouldn’t mind leaving a quote in the comments, that’d be very helpful.
I bought the book when it first came out, and I was in communication with the author, Christos Pandion Panopoulos, via a Facebook community. The English translation is riddled with errors, and I volunteered to find them all and offer corrections as they were planning an e-book version of the text where they would be able to correct all of these errors. I do not believe the e-book has come out, yet. In any case, through this communication, I was able to get some insight from the author on some of the more controversial statements in the book.
From what I recall, the reason that Panopoulos and his group believe that one should never use a picture (two dimensional artwork) of a deity on a shrine is because the deity literally inhabits a statue (three dimensional artwork) that is on a shrine but cannot do so with a two dimensional object. I have had many statues with shrines, and when I have felt the presence of a god, I have never felt it to be in (or only in) a statue. I have always felt it near me, behind me, in front of the shrine, perhaps even filling the entire room. I don’t think a physical vessel is necessary to hold a god. I think they will come if they choose to, and I don’t think any physical object can hold or contain them.
In my opinion, I think the Labrys community is reacting to the use of ikons in Greek Orthodox Christianity and in wanting to set themselves apart, they have come to believe that pictures are bad but statues are good (whereas in the Greek Orthodox Church, ikons (pictures) are good, and statues (idols) are bad). In other areas of the world, we react to other things in the dominant religions around us, either incorporating them into our practices or rejecting them wholeheartedly based mostly on our own personal histories with those religions.
If you are considering artwork for a shrine, consider why you want it. Is it a gift for the god in question? Is it beautiful and inspiring? Does it remind you of your prayers in a mnemonic kind of way? If any of these are your reasons, that I don’t think whether the piece is in two or three dimensions really matters. If you really want to know if a particular piece is ok for a particular shrine, the best advice that I can give you is to get divination done by a trusted diviner. The gods can and do make their opinions known. You do not have to believe everything you read.