So this is all kinds of wrong. When you make steel, you typically use 99+% pure oxygen - modern mills do air separation and reject nitrogen and argon (which makes steel brittle when it's dissolved in) and basically anything they can reasonably separate out but oxygen.
But furthermore, it's not radioactive oxygen isotopes that get into the steel in the first place - they're scant to non-existent in nature, since all three common isotopes of oxygen are stable and most of the rest decay in seconds. It's other radioactive isotopes in the air from the bomb tests.
99+% isn't 100%, and it turns out those tiny fractions of a percent of junk contain the isotopes that are the real problem, namely Cobalt-60 created by the nuclear tests. Carbon-14 isn't nearly as big of a problem, since its decay mode is just beta and can be designed around, but the gamma decay from Cobalt-60 contamination is much harder to deal with.
Furthermore, because of Cobalt's position on the periodic table and the desire to have a small amount of cobalt in steel anyways to give it better working properties, it's not something that's easily filtered out, even in processes that reform steel like vacuum remelting which exist to make mechanically harder and better quality steel by slow melting and recrystalization. Once the Cobalt's in there, it's in there - you just have to wait for it to decay.
As it turns out, we're in luck, most of the fallout from those bomb tests has passed through numerous half-lives and is much less of a problem today than it was in the 1980s and 1990s when the low background stuff became such a hot commodity. So it doesn't really matter as much that we're running out. Furthermore, oxygen separation technologies and cryogenic liquid handling have improved, so we can do an even better job keeping contamination out. If someone wanted to set up a low background mill, they probably could do it today with commodity molecular sieves and centrifugation of the oxygen rejecting all but the light fraction...