There is ongoing research looking into the effects of nut consumption during pregnancy. It is generally accepted now that consumption of peanuts during pregnancy may, in susceptible individuals, be linked to peanut allergy in children, and also to an increased risk of asthma and eczema. It seems that avoidance of such potential allergens during pregnancy, and exclusive breastfeeding, may reduce the risk of asthma and eczema, and delay the onset of these diseases when they do occur.
Peanuts are a different class of nuts from pistachios. Pistachios, along with almonds, cashews, hazels and brazils are tree nuts and current advice suggests that to eat these in moderation in pregnancy is fine. There is certainly no evidence to date that suggests that there is any great danger from eating pistachios in pregnancy.
If neither you nor your partner has any personal or family history of atopic disease (asthma, eczema, hayfever or other allergic problems), then it may well be that this is not an issue that you need to be concerned about. However, as I have said, this is an area of ongoing research and we don’t have all the answers at the present time.