So what happened is...
The builder originally, cunningly put a multi-wire branch circuit (MWBC) there, so he could power the two halves of the receptacle from two different breakers. He used a 2-pole breaker or two singles tied together.
Then, the service panel got full. To make more room in the panel, somebody changed out a bunch of single breakers for double-stuff breakers. When he came to this 2-pole MWBC, he ignorantly moved them to a 1-pole double-stuff without even knowing what that is or what it means. And indeed, be double-booked the neutral as you suspect.
As much of a wire-saver as the MWBC is, you don't want it. There are two problems with this: first, you have 240V that close to water, and second, you will want a GFCI on a kitchen circuit, and GFCIs capable of supporting MWBCs are expensive and not available in double-stuff.
The root problem is the panel is full.
This sort of hacked mistake/compromise is one of several things that makes too-small panels dangerous. Another is the impossibility of fitting AFCI and GFCI breakers. I am famous for wildly oversizing panels, I'm not being funny - my goal is to avoid problems like these.
The quick fix
The path of least resistance is to nut the red and black together in the service panel and pigtail it to the same exact breaker, i.e. One half of a tandem. (Or if your breaker is legal for 2 wires, there you go.) This is not paralleling as long as the tab is broken off on the receptacle. (If someone ever changes the receptacle and forgets to cut the tab, different deal, now you're paralleling.)
This solution will play nice with GFCI breakers.