I emailed California Olive Oil about shared lines with nuts. They said there's nothing on the lines but olives. The relevant part of their reply is below.
"Thank you for your inquiry – I understand your concerns, as a number of my family members have severe allergies! I am very pleased to be able to tell you that Our EVOO is certified as 100% natural EVOO by the COOC and that our equipment is dedicated to processing our oil and nothing else! Our Mills process only olives, and we have strict rules that do not allow food or drink in the milling area. Every possible precaution has been taken against any cross-contamination.
We are audited by the state of California regularly. We are SQF certified, Kosher and non GMO certified. All of those audit systems focus heavily on controlling cross contamination."
Thanks. I'm going to look for this brand. I use philipo berio now and it's fine but I like other options too since EVOO is so expensive.