Prevent "is this you" popup on my phone
No. There's no way you can prevent it. It's a security feature implemented by Google as pointed out in comment

If security can be relaxed there is no security

In your case with people joining in and leaving all the more reason - think of it as you are running a small company with employees using a common mail account - you wouldn't want unauthorised access

That it's a low value account to you is not relevant given that it's your account and Google security policy rightly does this