D-23 does not ordinarily behave the way you describe. Properly compounded, it is a very well behaved developer. I have used a similar divided developer, D-23 modified with a larger amount of metol, and never had any sort of fogging.
I have never seen that kind of fogging. (Except one time when I screwed up compounding it, and put the wrong chemical in instead of sulfite.) W/o a preservative it may still create an image, but you may not like it. I got a lot of fogging.
A couple of ideas.
1. Problem with the film? Have you tried a different batch of film known to be fresh? D-23 just isn't that active. And it is quite clean working.
2. Mislabeled chemicals? Maybe the film is fine but you have unknown mix of developer. How does this film develop in pre packaged D-76 1 to 1 or 1 to 2? Does it show much of any fog? I would suggest that if the film is good in prepackaged D-76 that the film may be bad. Either fogged through very bad storage , airport x-raying gone crazy, age...
3. Are you replenishing it (KodakDK-25R) and maybe using it beyond the point it should be tossed? Suggested limit is 25 rolls/litrer, then throw away.