I don't see why being a non-profit means being also a no-revenue.

Add a paid layer, with premium features. Make premium features a gift option to other accounts, so that it could be a token of appreciation.

Add a paid layer with the only paid feature being a "proud supporter" badge. Surprisingly many people take pride in that when it costs them a $5.

Add a donation button, run donation campaigns. It works for Wikipedia :)

There's no need to avoid being paid.