I've seen both in newspapers when it comes to the subject of global warming. Confusingly, "rising sea levels" seems to be used more frequently. For me, it's much easier to understand "rising sea level", an uncountable noun used to describe a concept of the rising sea, than to imagine it as a countable noun, "sea levels." How does "rising sea levels" even mean? Aren't all the seas that would be affected by the melting of the glaciers connected with each other in a way? How can their "levels" be separated from each other when the amount of water in seas on the earth rises?
Rising sea levels is factually correct, even if counter-intuitive.
As long as (the incorrect) "rising sea level" does not have clear and obvious grammatical superiority, the (correct) plural should be used.
See the Wikipedia article, especially the section showing factors which change Sea Level in a locality, for some ways to overcome your intuitive (and incorrect) idea that Sea Level is the same everywhere.