In a certain way, it is important.
Christ was a certain person who actually existed in a given time and place, and had a certain general ancestry—ie Jewish.
If we deny those facts, then Christ is no longer a real person but a mythical one. He actually had a body. One body.
No 33 year old (for discussion sake, let’s say at the time of the Passion) human being changes appearance to match that of other people with whom he interacts.
Artistically speaking, people tend to portray Christ according to their own ethnic comfort zone. In art, that’s fine.
However, in the realm of theology, it is absolutely essential that we affirm that Christ was a real human being (insert hypostatic union). He did not come to earth as a vision or a mythical creature that changes appearance.
Some people like to say that Christ’s earthly body might be anything that makes one comfortable. While we can express that idea in art, we must understand that this notion does not carry-over into the actual physical historic Christ.
We do not know exactly what He looked like, but we do know He appeared only one way.
We cannot deny His Jewish identity, and that means Jewish genetics and appearance. We cannot deny that His physical appearance was that of a first century Palestinian Jew; because any denial of that necessarily leads to a denial of the Incarnation.