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Currently I am running a semi compact 52/36 up front and a 11-28 at the back. I'm planning on getting a 11-23 cassette for criterium races, and have the 11-28 for hillier rides.
Will there be any issues with chain length when swapping back and forth between the two? If I leave the chain length as is (optimized for a 11-28), will I run into any problems when putting the 11-23 in?
It should be fine.
The chain will be a little bit longer than necessary when using the 11-23, which may give some droop if you're running bad gear combinations (e.g. small chainring+small cog), but nothing serious.
Never run with a too short chain. A bit long is OK.
In this particular case it will not cause a problem. As long as chain length is right for 11-28.
Chain is too short, if chain is too short to raise to bigger gear. For example if 52x23 is ok, but it might still be too short for 52x28, not vice versa.
Chain is too long, if chain is rubbing against derailleur cage. It would cause noise, wear the parts and affect precision of gear shift.
Logically, the longer chain cannot cause a problem. This is because your 11-28 cassette already includes an 11-23 cassette inside it. The longer chain is working just fine with the 11-23 which are there now. It will work exactly the same if 11-23 is the entire range! If you have no droop with 11-28, there will not be droop with 11-23 with the same chain length.
The other direction doesn't necessarily work, of course. A chain length that is fine on 11-23 might not be long enough to go around the larger cogs of an 11-28, causing a disaster.
Since your derailleur has a spring-loaded tension wheel, extra chain length doesn't matter much. Shifting can be excellent at a range of tensions. So while the 11-23 gives you the opportunity to shorten the chain, you don't have to take up the offer.
If you make the chain as short as possible, then you can't do an emergency repair out on the road which involves splicing out and throwing away a damaged pair of links. (Or rather, you can, but probably shouldn't).
