First (legitimate) login attempt always fails (silently)

Since having the suspicious login app enabled, every first of my own login attempts fails. Login page simply reloads, without any message. Second attempt always works.

Nothing in logs.

Any idea how to track down this issue?
Is it maybe a well-known side effect of this app?

See if you can find a related issue in their github repo. If not, file an issue there and then link it here.