I am doing the Sisters of Eve storyline mission. I am Amarr. When I enter Arnon (Gatllente space) where the Sisters of Eve, I am warned that I will be attacked by Federation Navy. I have (with help of Diplomacy Level 4) a Gallente rating of 0.32 but a Minmatar rating of -0.53 (due to Faction Warfare against Minmatar). If I hang on for about 15 seconds, I get attacked.
You answered your question with this… as an enemy of the Minmatar you are also an enemy of the Gallente so will be attacked in their space just as you are in Minmatar space
Changing standings won’t help you here. While you’re enlisted in FW for the Amarr Empire you will always be permanently at war with both Minmatar and Gallente