I think I know the answer to this one, but hey ho. 
I’ve had iPhones all my life, but am being tempted by phones like the Librem 5 or a Samsung Galaxy running Replicant.
Since these are not Googled-Android and don’t have the Play Store, would I be able to install the Monzo app?
I think if you got the APK from somewhere reputable it would probably work - I’m not sure that Monzo actively blocks this sort of thing.
But two thoughts / issues / questions:
tl;dr: will quite possibly work but 
at your own risk
Hey 
I’ve started uploading the Monzo APK to apkmirror.com … They’re the biggest most trusted distributor of APKs but ofc, it’s entirely your choice 
https://community.monzo.com/t/monzo-for-android-beta-channel-changelog/10207/528?u=nexusmaniac
I run on the beta channel so most of the uploads on apkmirror will be beta releases but monzo is incredibly stable regardless.
Hope this helps!
I do use APK mirror every now and then but I’d be seriously hesitant to download a banking app from anywhere other than the Play Store.
If anything, I’d install the Play Store on the device and then get Monzo.
Would you really want to trust downloading an unsigned APP from the internet? If it were a direct download from Monzo, sure, but I’d be very worried about third party ones, personally.
This would be my biggest concern. It would be nice if Monzo could publish hashes of the APKs somewhere on their website, that way anyone can verify whether an APK downloaded from third-party sources is legit.
Haven’t heard of either the librem devices or replicant OS so have bookmarked them to research a bit more.
The monzo app works for me running Lineage OS on a Samsung galaxy series device.
Yes, I’m not sure if my appetite for risk covers an unverified APK. 
I wonder if Monzo would consider publishing it themselves; an official source.
I’m glad to hear that! 
Did you install it from the Play Store?
What you could do, which is a faff mind you, assuming you cannot get the play store installed on your device(I got it installed on an Amazon Kindle)…
Setup an emulator on your PC , bluestacks may work or the android SDK which I think comes with one.
Install Monzo, then use an app to export the APK. APK exporter or something
That way you know exactly where its come from!
Or do the same on a friend’s android device
Will the phone have Google Play Services? I’ve ran Android phones Google-less before and most apps worked, but things like notifications may not work (as they may be based on the Google messaging system/firebase)
It’s hard to find an emulator that has Google Play to download the app in the first place.
Genymotion? That’s open GApps anyway.
I’ve done this using AnBox on Ubuntu and installed the Monzo app, but when I try and sign in it wants to open an email App for the magic link. So I’ve then installed gmail on Anbox but that won’t run without Google Play (which I can’t install). I feel like the old lady who swallowed a fly.
You shouldn’t need an email app, that button’s just there for convenience. I’ve done it several times from webmail.
Cheers lmcm - watch this space - I’m going in
Tapped on link in email into two browsers:
Firefox won’t open it - Firefox doesn’t know how to open this address, because one of the following protocols (mondo) isn’t associated with any program or is not allowed in this context.
You might need to install other software to open this address.
Chrome takes me to Launch icon but nothing happens when I click it 
Oh dear 
I’m out of advice I’m afraid, that’s always worked for me.
OK. The way I’ve got it to work is to install Firefox as an app and then paste the magic link into that - it works!