I don't know what women's soccer policies are but according to the Timbers website
Sealed or empty water bottles and soft-sided single juice containers for children are permitted into Providence Park.
At baseball games (MLB, anyway), they only allow full, sealed containers of water, but you can always refill at a bubbler inside. This is relatively new, as they used to not allow anything (although it was always easy to sneak in cans of Surly to the Metrodome since you always needed a jacket and could stuff them in the sleeves; it'd be harder now with metal detectors). There's now a cottage industry of guys who set up outside the ballpark selling bottles of water for $1, which I'm willing to pay, because I'd rather pay them $1 than pay $5 inside.
Back in 2002, the Red Sox played a double-header. July 1. 90˚. Not only did they refuse to let you bring water in, but they ran out of water to sell, and then refused to fill cups with tap water (but were glad to sell you a coke or a beer). Dehydrated kids. Angry parents. They were rightfully dragged through the press for that one, and started giving out water. But, like the airlines, they'd rather not tell you.