I don't think the voting part would be a problem for anyone. The issue that the article is bringing out is is it OK for non-mormons to be prohibited from drinking caffeinated drinks while serving as poll workers? Do poll worker requirements stipulate staying on post the whole time or do they allow for adequate breaks to coffee-up? As colorcountry noted, there are dress requirements for women entering these ward houses that appear to be waived for the poll workers. If this religious requirement can be waived, why not the coffee/coke requirement too?
That is why I stated that the polling place should be moved.