Tranquilo, hermanos. There is a middle ground here that I think satisfies most concerns.
For private sector jobs, including DoD contractors:
You must answer all questionnaires and interview questions truthfully. But your resume itself can include or omit whatever you want, so long as you aren’t making stuff up. You don’t have to list your side bartending gig, you don’t have to list that you sell crafts on Etsy, you don’t have to include your reserve job. It’s a resume not an SF-86. I’ve reviewed hundreds of resumes in the past 10+ years and the format can be whatever Millennial jobseeker Josie/Josh wants it to be (I’ve seen some wild ones).
After you get the official written offer letter for a new job, but before your start date with the new company, that’s a good time to let your recruiter or HR office know if you are a SELRES or VTU reservist (or really any secondary employment, as most employers require you to submit and get approval on secondary employment IAW their HR policies). Lots of states are “right to work” states and you don’t want to be arguing in court about getting your job back while you’re out of a job. No sense hiding or delaying the inevitable truth from your future employer. If they choose to rescind the offer letter before your start date, and the only reason is your newly disclosed reservist obligations, call your attorney.
For government jobs, in my experience (and I do have some as a former lowly GS) the USAJOBS application forms are pretty thorough, meaning you’ll probably be asked if you are in the military in any capacity. Be honest to the extent you are asked about SELRES or VTU obligations.
I think there is a fair argument to be made that you’ll never be docked for omitting that you’re in the non-VTU part of the IRR (assuming you aren’t actively planning to jump on ADOS orders or reaffiliate with the SELRES from the IRR). That’s like omitting the fact that you registered for the SSS and are theoretically eligible to be drafted in event Congress reinstates the draft and then starts calling lotto numbers. There is probably a bunch of case law on that from the Vietnam era and employers/draftees.
You’re also allowed to request mobilizations be canceled for individuals if you can make a case they’re more valuable to the govt in their current position.
I’ve seen this happen, but only with govt civilians. Most contractor companies are told to pound sand if they decide to play that card (bc the SOW would have to state that the govt considers the contract employees to be mission essential staff).