Stick with it. You do not have to agree with the direction of the committee and their politics. You join the AOA because when you slide gracefully off a runway in a foreign land there will be a legal representative in that country to try to get you out of jail, and to bring you food if they cannot. IFALPA works at times like that.
Your company will be embroiled in a political dance and as you are expendable in the big scheme of things will most likely leave you twisting in the wind.
It is not expensive insurance to be part of a bigger organisation.