Earlier quoted context omitted.
Sad truth. I'd like to see something label itself as a public-interest group and be able to trust it immediately, but it's not as simple as that.
It's not very difficult either. For most of these organisations, you can just check their Financials page, and it's very clearly stated. Example: https://www.accessnow.org/financials/ https://cdt.org/financials/ Trusting anything immediately is a bad habit to develop anyway.
For example, in the links you provided, we can see that AccessNow is supported by Google and Facebook, but also by Mozilla, which is generally considered to be a strong privacy advocate. Similarly, CDT is supported by Google and Facebook, but also by DuckDuckGo and Mozilla.
So what can we conclude from this? I'm not really sure. It could be any of:
1. Mozilla, DuckDuckGo, etc. are supporting organizations that are working against the interests of privacy.
2. Google and Facebook actually care about privacy.
3. Privacy is a complicated issue and there aren't really well-defined "sides" to take.