Philosoraptor

Because they were investigating the source of the plague. They knew they couldn't change the past, but they wanted to find patient zero and the origin of the virus to try to find the cure in the future.

Why would they do that if they didn't think they could change the future?

Because you can change the future. We do it every day. It's the past you can't alter, unless you're a revisionist historian. They were seeking information about their past that they could utilize to alter their future.

When BW landed in 1990, he didn't believe he could stop the outbreak that hadn't happened yet. They clearly didn't believe they could change the future.

That wasn't his future. To him, it was the past. It wasn't a particularly well done time travel movie, but the nod was there. He was traveling back to be a participant in PRIOR, pre-established events. He remembered seeing his grown up self shot at the airport because that happened. In the past. Not change-able. The people living up in the present, though, could utilize anything he brought back to affect THEIR future. The part of time that wasn't written, yet.

The problem is that their present and future is someone else's past. If they couldn't change their past, they would not be able to change someone else's. Either everything is set in stone or it isn't.