Hi,
some thoughts from my side. This is also what I always recommend people who write mobile apps for the Free Software projects I’m involved in.
Free Software doesn’t mean “gratis software”. Free Software developers deserve to earn money with their work the same way people who develop proprietary software do.
Therefore I always recommend people to offer their app on the Google or Apple app store for some money. 0.99€, 1,99€… Something like this. Not super expensive but a price everyone can pay easily and roughly on the same level people pay for similar proprietary apps. At the same time publish the app on F-Droid and maybe even the APK on your webpage for free. The gratis version should contain a donation button/link.
The reasoning is simple: People who want to have the convenience to install stuff from the regular app store should pay you some money the same way they pay for many other apps as well. Often this are also people who don’t know that much about Free Software and are not used to a “donation culture”. People who use F-Droid (or download the app directly at you homepage) are typically more connected to the Free Software community and might be more open for donation. So ask them for donations in return for your great app which they can use for free.
This way you get the best out of both worlds. According to the play store, K9Mail has +5Mio installations. Let’s assume only half of them would buy it for 1€, this would leave you with 2,5Mio € (minus taxes and what google gets). Still, probably a nice amount of money. Plus the donations from some of the F-Droid users.
On a education level it teaches people that Free Software doesn’t mean gratis software and that the freedom respecting, add-free and privacy respecting software they get should be worth at least as much as what they pay for way worse apps.
Therefore I would say: Don’t be afraid of asking for money and also take the easy money. Buying a app with one click is for many people way easier (and it is what they are used to) than creating a LiberaPay account and setup a regular donations. Some “hard core” fans might do it but only a few regular users will do so.
I hope you will get enough money to continue to work on the app. I don’t know what I would do without k9! 