I would ignore what other people are doing. The charity sector is not always known for it's super-efficient and industry leading digital marketing activities. So although the advice that John Mondt gives is sound for many industries, he is right to include the phrase 'what's working' for them. So don't just copy their link profile or go after links before carefully analysing them for quality and their potential to be relevant in the future. I work in Dentistry and copying other dentists link profiles is more likely to land me with a penalty than take my DA anywhere special.
Charities tend to be filled with people (at the senior levels) who have pretty impressive backgrounds and CV's. Also you're in a very strong position because charities are good for the world so no matter who you contact, you're always going to be coming from a place of positivity and wanting to make the world a better place. This is huge. So I would round up everyone at your charity on the board who belongs to any university, trusted organisation, professional body or other trusted domains and reach out to them for guest posting ideas and shameless plugs of your organisation.
Link building for a non for profit is about just putting together a great pitch about how you're helping the world and then asking for help to spread the word. Don't be afraid to be totally authentic and honest about wanting to improve the visibility of your website (short of asking for links which is against the guidelines)
Hope this helps. But I was looking at a big charity just now and there are CBE's on the board, people with honorary degrees from universities and people who are members of huge and trusted organisations. So as a linkbuilder, i'd reach out to those people and put together a strategy of how to leverage those relationships to gain links. Or in this case 'do PR' as white hat linkbuilding and PR are now pretty much synonymous. (used to say not synonymous, sorry, PR and linkbuilding are the same - that's a typo)
hope this helps. PS: I love helping charities so maybe hit me up and I could help you in more detail. Obviously i'm not going to charge you but a mention from a charity website is always a great thing for us. We just did a huge campaign for international women's day that bumped our DA three clear points. Win!