Is it impossible for now to run Wireguard VPN server container on BalenaOS?

For pi3 you could try hardcoding the architecture in the FROM linuxserver/wireguard:... field to FROM linuxserver/wireguard:arm32v7-latest because it looks like the arm64v8 arch was pulled by default.

gcc: error: unrecognized argument in option ‘-mabi=aapcs-linux’
[wireguard]       gcc: note: valid arguments to ‘-mabi=’ are: ilp32 lp64

I don’t think the same solution will work for pi-zero because linuxserver doesn’t have an armhf architecture but you can try with arm32v7 and see if it builds anyway. Also, I haven’t tried any dev kernel header packages myself so there may be other differences I’m not aware of.

You may also run into this issue that I don’t have a solution for quite yet.