For festivals: Check the history of the NGO you want to have at your event before inviting them. It might be that NGOs face criticism (e.g., questionable activist actions, involvement in the misappropriation of donations). Actually, this does not affect you as the organizer directly. And you should differentiate between festival core values and your own opinion. However, should media representatives become aware that such an NGO is presented at your event, this can draw your event into the case and eventually impact the reputation of your festival. In addition, it usually takes a lot of effort for outsiders, such as your audience, to understand such inconsistencies. You won’t have the capacity to do damage control then. To avoid a shit storm, better check each NGO with a quick internet research before you commit to it.
For NGOs: Festivals have values that they represent and implement as good as they can on a large scale. Familiarize yourself with the festival. What have they done in recent years? Which sponsors do they have? What are their values? Do these values align with these of your NGO?
If you don’t want to cooperate with a festival because they have sponsors with dubious reputations, that’s okay. Explain the matter honestly. But also understand that the festival likely won’t get rid of their sponsors just because they are not in line with your organization's values.
Check out the United Nations’ database of NGOs to find out more about an organization:
https://unric.org/en/info-point-library/online-databases/non-governmental-organizations/ The EU also lists some pan-European NGOs:
https://ec.europa.eu/social/main.jsp?langId=en&catId=330