I've read that ppm in he headspace translates to ppb in the beer. Maybe somebody with better math skills than me can show the work.
The trick is in the definition of "ppx." For gases, it's the partial pressure of the gas (or parts per x by number of molecules, same thing.) So if the total CO2 pressure is 2 atm and you have 1 ppm O2, you have a partial pressure for O2 of 2e-6 atm. On the other hand, ppx in liquids is measured by mass, so 1 ppm O2 means 1 mg of O2 per kg of beer.
The Henry's Law constant for O2 at 25 C is 1.3e-3 mol/L atm. So at equilibrium, 2e-6 atm of O2 will give you a concentration of 2.6 nM, ~80 ng/kg, or 80 ppt. 50 ppm O2 in your tank will give you a whopping 4 ppb in your beer. On top of this, it takes time to even get to equilibrium; gases dissolve and diffuse slowly. Consider the days/weeks it takes to force-carbonate using a set-and-forget approach.
However, things are much worse than this. The scenario brewers should consider is that oxygen dissolves into the beer and reacts, which means more oxygen can dissolve, which also reacts ... until all of the oxygen is used up. So the thing to do is to determine the total mass of oxygen the beer is exposed to, and from that calculate what the concentration in the beer would be if all of that oxygen were dissolved.
If you're force-carbonating your beer, the headspace volume doesn't matter as much as the volumes of CO2 used to force. Normal carbonation levels mean 1 L of beer needs 2.5 L of gas (at atmospheric pressure). If that gas were 100% O2, it would have a density of ~1.2 g/L, giving you 3 g of O2 total. If you're at 1 ppm, this means that over the course of force carbonation, you've exposed your beer to 3 ug of O2 ... and 3 ug of O2 per liter of beer is ~3 ug/kg, or 3 ppb.
If your CO2 is ~50 ppm, this means 150 ppb O2 in your beer, which is not a deal-breaker, but it is not negligible by any means. It's certainly worth thinking through the implications -- can the oxygen exposure be lowered, will the beer have a short shelf life, etc.
If you naturally carbonate your beer (spunding or keg conditioning) you can lower the amount of gas the beer is exposed to. Now the only CO2 coming from the tank is what you push into your headspace for serving, so the ratio of headspace volume to beer volume matters. The math is very favorable with a full keg and 10s of mL of headspace, but less so with a near-empty keg and 10 L of headspace.
Let's say 1 L of headspace and 20 L of beer. Let's say you're serving at 2 atm absolute pressure and 50 F, where if it were 100% O2 the density would be ~2.5 g/L. So at 1 ppm, you've got 2.5 ug O2 in the headspace, and 2.5 ug in 20 L of beer is ~0.1 ppb. With 50 ppm in your tank, that's 5 ppb for your beer.
However, when your keg is half empty, you've now got 25 ug of O2 in that 10 L headspace, and it needs to dissolve in only 10 L of beer, so 2.5 ppb. With 50 ppm in your tank, your beer is now at 125 ppb, which again is about where you start to think hard about things.
(Things are worse if there's effective mixing of the gas in your keg with the gas in your tank -- that is, as oxygen dissolves in your beer, more oxygen from the tank comes into the headspace. My gut feeling is that this is going to be very slow and can be ignored.)
TL; DR:
- If you're force-carbonating, typical oxygen levels in your CO2 tank probably do matter. With 50 ppm O2 in the tank, you're looking at ~150 ppb in the keg. This is in the ballpark of current practice for professional breweries, so you should probably expect ok but not stellar results: shelf life measured in weeks or months.
- If you spund (or keg condition), 50 ppm O2 in your CO2 supply will have a negligible impact when your keg is nearly full, but will become more important as you dispense. When half-full, you again have ~125 ppb in the keg.