your local arts events are often sponsored by local businesses and philanthropists

Do you or they necessarily approve of those businesses? Is that implied?

but if you or I donate $10 I wouldn’t call that a sponsorship

Then are people getting carried away with their imaginations? When I see a “we sponsor” section with logos/names, I don’t assume a substantial amount: could be token for all I know. Quibbling over that when it’s true feels like arguing over inconsequential merit badges.

Donation recipients should be able to take money from donors who should be able to declare that truth.