I have foam filled bladders in a couple of my race cars that I've had to replace due to normal aging of the bladders.
I can attest to the fact that the soft open cell foam is cut from sheet and hand placed inside each of the bladders.  As such it provides no strength what so ever to resist splitting of the external aluminum tank.  It does, however resist sloshing and should also slow the release of gas in the event of a catastrophic failure of the bladder, case or cap should the vehicle in which it is housed become seriously impacted, overturned/ lose the cap.
It seems unlikely to me that oil that is dissolved in gasoline could become pulled out of solution preferntially by the foam, although a temporary segregation of the oil in the initial stages of pouring it into an otherwise empty tank seems possible , but without any lasting consequence.  Then again, this is just what seems likely to myself, and is probably better off being properly checked.