What the subject says.
I want to power a rack of commodity servers with 110v power supplies from single NEMA 14-50 outlet. I plan to distribute servers between L1 and L2 such that even at full tilt current on either side doesn't exceed 50A. However load is likely to be uneven most or all of the time.
Is this a problem?
I really wish they'd named this group "electronics engineering". Because your question is definitely about electrical engineering!
Based on first principles, you should be OK. But it's going to vary by region, and possibly with the personalities of your local inspectors. If it were me I'd want to consult with an electrician in my area about what will meet local codes (and make inspectors happy).
I think you may be violating one of the tenets of the electrical code, which is that you need a circuit that's fused to match the cord running from plug to load -- so if your rack breaks that 50A service into a bunch 15A sockets without further protection, it's probably not going to be up to code.
You may need a sub-panel someplace, broken out into individual 15A circuits -- either in your rack, or on the wall where you're planning on putting your 50A socket.
Yes, it's OK. What do you think happens with all of the other 110V outlets in your house? Even something that you would normally plug into such a socket, such as a clothes dryer or a cooktop, will not always draw the same current through L1 and L2.
And despite what TimWestcott says, the electrical code doesn't care what happens beyond the wall socket — it is only concerned with "permanent" wiring that is part of the building structure.
However, he is correct in that anything that "looks like" a 15A or 20A socket should really have appropriate protection — so your rack should have an internal distribution panel with suitable circuit breakers.
Drawing Uneven Current Is Fine
On a NEMA 14-50 plug, it's typically the case that the load on the two hot legs are uneven, and the neutral is used to return the difference current. If the load on both hot legs was exactly the same, neutral wouldn't be needed at all, and you could use a NEMA 6 series plug instead.
Connecting 15/20A Receptacles to a 50A Circuit Is Not
You don't mention how you plan to break out from your 2x50A feed into individual 120V circuits to send to your servers, but if you're intending to directly wire from the 14-50 plug into some standard receptacles, don't do that. Those receptacles need to be breakered for 20A at most, so that if one of the server power supplies suffers a short circuit, the breaker can trip before the receptacle melts and catches fire.
If you're using standard electrical distribution hardware, you should fit a subpanel between your 14-50 plug and your receptacles. Alternatively, some server power distribution hardware has circuit breakers built into the receptacles themselves; this is also fine.
Consider Feeding Your Servers 240V
You mention that you're using standard commodity servers -- in 2019, that means they will have universal-input power supplies designed to be used anywhere in the world, and will accept a voltage input of 100-250V. Double check the labeling on your servers, but it's extremely likely that they will be perfectly happy with 240V instead of 120V. If you do this, you will guarantee balanced current on your two hot legs, and you will make maximum use of the power you have available. Most likely, your servers power supplies will also run a few percent more efficiently as well.