Have you considered shaving your butthole area? I’m told that helps for cleanliness issues.
Or co-opt panty liners instead. There are many brands out there that are light and almost weightless–you won’t know it’s there, but your undies will not be soiled.
I must say, though, I second the getting checked out by a doc. I have 2 boys and a husband and I’ve never had this problem with their laundry (short of the times when potty training). The feminine side of the laundry does not suffer from this, either…
The only problem with this is if you fart while sweaty, you can trap the air bubble between your cheeks. Then you get that little ball of stink racing up and down looking for a way to escape.
Pardon my French, it’s been nearly 20 years, but voilà que le Ministre de l’au-delà voudrait administrer a l’au-dessous…
Put me in the camp of fart, streak, discard and repeat. Always repeat.
Wouldn’t it be more fun to get someone else to do that? I put enough nicks in my neck as it is…
Next thread: How do I remove blood spots from my y-fronts?
Your work makes you meet other people in underwear and you wear white briefs? Do people over age 9 wear white briefs? Get some colored boxers not for the skidmarks but for your own presence.
(and trash away anything shitstained that you cannot clean)
This is so wrong in so many different levels. First, why would your neighbors be looking inside your house? Why would it be better that they think you are wearing speedos in the house? Why would you be happy with invisible shit on your clothes just because strangers cannot see it?
Yes, I have a preference for white briefs. Briefs, because boxers are not comfortable under jeans - the jeans are too tight and just cause the legs of the boxers to roll up around the pockets, and white because I prefer them. Yes, I am over the age of 9, so I think we can safely conclude that there are people over the age of nine who wear white briefs. 
An amusing story about a friend who did a scene for an acting class that involved both actors being in their undies for the whole scene. Ron wore boxers on the first day, and every time he sat down or bent over, he showed his goods. The acting teacher had to pull him aside and say “Even if you feel boxers are better for the character, you should wear briefs or jockeys under them, or just don’t bother with anything - flashing is more distracting that just showing.”
As far as the medical question goes - No, I don’t feel it’s a medical problem, though I stand to be corrected if one of the medical dopers feels it is something I should bring up at my next check up. (I’ve already reached the age of prostate exams, so it’s not like there’s anything taboo between me and my GP anymore.) The thing is, if I were leaving marks after showering, bathing, using the bidet, that would be one thing - I’m not. It is only when I don’t bathe after defecation that I leave a mark - other people’s preferences and results from anal hygiene may differ; I just find that bathing does a better job. Maybe I have more wrinkles to my sphincter than the average person.
At any rate, thank you for the suggestions, and I’ll see if any of these are the magic bullet I’m looking for.