I have an 11 speed 11-30 rear cassette that I would like to replace but cannot seem to find an 11-30 anywhere. Can I safely replace this with an 11-28 or an 11-32 without replacing my rear derailleur?
If the OP's bike has a short cage Shimano rear derailleur, then officially, the maximum cog size is 30t. Going down to 28t is definitely fine, but going over 30t is not technically OK. Shimano's compatibility specifications are known to be conservative, however, so in practice, a 32t cog should work. I would caution against exceeding the maximum cog size by more than 2 teeth, unless you also install items like Wolf Tooth's RoadLink, which extends the derailleur hangar.
I would very cautiously disagree with @BenStokes that you must necessarily lengthen your chain. The OP may find that your chain is long enough to handle the 11-32. I recently installed a pair of oversized pulley wheels on my road bike. The official recommendation is indeed to resize the chain, but in practice, my chain had adequate length to shift into the big ring, big cog combination. I would suggest that the OP can very cautiously try to shift into this combination in the bike stand (and not on the road). If the chain is at all reluctant to make the shift, stop moving the crank immediately and re-size it. With the amount of force you can generate with your hand, then even if the OP's chain is too short, the OP won't damage anything if they stop promptly. (This is why I suggest not trying this on the road; your legs can produce enough force to do considerable damage.)
Conversely, if the OP's bike had a medium cage Shimano derailleur, then technically, the smallest large cog is 30t, and an 11-28t cassette isn't officially compatible. However, I am actually running an 11-28 with a medium cage rear derailleur right now.
I have no current experience with SRAM or Campagnolo, but I believe the same recommendation (that you can exceed the official specs slightly) should hold true. I used to run a short cage Campagnolo 10s rear derailleur with a 13-29 cassette, i.e. exceeding the maximum tooth count by 4. I did this on advice received on forums that this could work, depending on the bicycle. Again, I would prefer to recommend that people don't exceed the maximum cog count by 4 teeth.
Going down to 11-28 should be fine. Going up to 11-32 will probably be fine. If it were my bike, I would just give it a try and hope for the best, but I tend to be a little cavalier about the possibility of breaking stuff.
You'll need to check the specs of your derailleur. There should be a min and max low cog listed, make sure you are within that. There should also be a max front difference listed, meaning the difference between the largest and smallest (front) chainring can't exceed that number.
For example: This derailleur... https://bike.shimano.com/en-US/product/component/duraace-r9100/RD-R9100-SS.html Can handle the a low sprocket from 25T-30T, with a max front difference of 16T.
If you decide to go with the 32T, you'll probably want to add one chain link (one inner and one outer), and since it is a new cassette, I'd recommend a new chain too unless your current chain is pretty new.