I'd much rather do a take-home project at my own pace funded by the company, seeing as how my personal GitHub is a barren wasteland (well...it was before I started working for an OSS company).
My current employer doesn't have explicit rules that I'm aware of, but early on, I asked our HR person if I could work on open source outside work and they said something along the lines of "what's open source?" Which, I mean, on the one hand what do you expect from HR, but on the other hand, the entire agency is concerned with operating, maintaining, and developing a software system.
If it's not on employer-owned equipment during core working hours, then I believe it's pretty difficult for an employer to enforce that kind of thing. I don't know how important to you working at that charity was or participating in open-source now is to you, but if you're willing to take a harder line of telling rather than asking, you might find that when push comes to shove, there might not be much they can do without drastically escalating the situation (not always an organization's favorite thing to do, even if they can technically win, which they might not be able to).
Obvious disclaimer about being a non-expert on this sort of thing, but really just wanted to point out that the first answer in this situation may not actually be the final one.
And its not really the "employment contract" in Anglo Saxon legal systems its pretty much assumed.
Also, running side businesses was not allowed.
Of course, the normal thing to do was just ignore the rules, because most likely nobody would notice or care. I explicitly asked for permission because I wanted to see what would happen.
This might require engineers unionizing, but it would be a boon to the field. Patterns buried in closed source vaults would be disseminated and innovation would surge. It might usher in a golden age of software if everyone were able to freely share their intellectual ideas with their peers and not have to worry about risking their health insurance and home in the process.