What do we a as a Sumarian reconstructionist organization have to do with Christian Gnosticism?

The answer is somewhat complicated:

adjective • relating to knowledge, especially esoteric mystical knowledge

The name was chosen because of its definition, not with intention to have any kind of relationship to Christian gnosticism.

However it’s easy to see many parallels between the æon Sophia and the goddess Inanna so we do think that she is a kind of folk memory of the goddess carried on in a later tradition. The parallels don’t end there and one could probably fill a book on them, but as many parallels there are, there are as many differences. So beyond sharing some similar ideas we do not see ourselves as related in any significant way.

Does Inanna need to be my patron to be a member of the temple?

No. The temple is dedicated to Inanna in the same way you might dedicate a building to the memory of someone who performed a great service for your town. Historically each temple would be dedicated to a deity, but they would not be the only deity worshipped within, rather they would be the focus of the temple’s structure and rituals.

Many of our rituals are based around the various myths centered around Inanna but she is far from the only deity we worship or recognize. After all, we are a on a polytheistic path.