Who does this stuff belong to exactly?

In the REPCONN center the Bright Brotherhood originally owned the stuff in the testing site. However, when they leave, it still counts it as stealing.

So, who am I stealing from?

In the epilogue it is said they come back, they don't leave forever., perhaps they paid the rent for the year

But anyway, because the owner is absent doesn't mean the stuff does not belong to him. Imagine you leave your car on a parking lot and when you return someone took it pretending it was abandoned

Most people leave home for work or holidays. It doesn't mean you are free to break in and take the stuff in their house

Oh I always thought they left forever. And besides the point is:

-I fought the nightkin for them, the least they could do is provide me some first aid

Yes they are ungrateful bastards.

They even betrayed the poor Chris Haversam after all he did for them

I hop you sabotaged their spaceship

Actually, YUP, the unofficial patch, removes owner of those items when the rockets have launched, so it's not stealing anymore. So, it could be considered something Obsidian forgot to do.