SpaceX would almost certainly do so if Russia would let them. They launched PAZ, which was a Spanish spy satellite and have launched several cargoes for governments like Qatar and Thailand.

Edit: just to expand on this a bit, SpaceX is and always has been a US federal government contractor. If you have a problem with that as a potential hire you probably do not take that job. But if the US government doesn't have a problem with a launch, SpaceX is also a money-making enterprise and I would bet they'd take whatever launches people would pay them for.