Again, why do you think that small local charities are immune to this? Unless you're a forensic accountant or have actually observed their operations, you have no idea whether a local charity is better than a national one.
In my "small local" charity work, I've been pressured by the Chair of Trustees to drop a bullying allegation against another trustee, and seen patronising and derogatory comments aimed at frontline staff. Trustee roles were dished out to rich mates of the rich trustees, not those representative of the community being served. Oh, and some horrendous misogynistic behaviour against a junior member of staff who was actually at risk, which I had to flag as safeguarding when no one else recognised it, and force them down the proper routes when they were acting with gross irresponsibility as an employer.
When I left, several staff contacted me with diatribes about how badly they were treated and that they wished they could leave too.
In my national level charity work, I've been emphatically told by the CEO themselves that they want to face up to any internal issues, and that I must not let any fear of damage to the reputation of the charity impede my work to improve things. They noticed that they didn't know me personally when I came back from Mat Leave and took the time to introduce themselves and chat about my work. It's not perfect, but it's streets ahead in terms of working environment.