How to redirect a user to a specific activity in Cloud Firestore?

Using two different collections, one for each type of your users isn't quite a flexible solutions. Another more simpler solution might be:

Firestore-root
   |
   --- users (collection)
        |
        --- uid (document)
        |    |
        |    --- email: "[email protected]"
        |    |
        |    --- password: "********"
        |    |
        |    --- type: "student"
        |
        --- uid (document)
             |
             --- email: "[email protected]"
             |
             --- password: "********"
             |
             --- type: "teacher"

See, I have added the type of the user as a property of your user object. Now, to get a user based on the email address, please use the following lines of code:

FirebaseFirestore rootRef = FirebaseFirestore.getInstance();
CollectionReference usersRef = rootRef.collection("users");
Query query = usersRef.whereEqualTo("email", "[email protected]")
query.get().addOnCompleteListener(new OnCompleteListener<QuerySnapshot>() {
    @Override
    public void onComplete(@NonNull Task<QuerySnapshot> task) {
        if (task.isSuccessful()) {
            for (QueryDocumentSnapshot document : task.getResult()) {
                String email = document.getString("email");
                String password = document.getString("password");
                mAuth.signInWithEmailAndPassword(email, password).addOnCompleteListener(/* ... */);
            }
        }
    }
});

Once the user is authenticated, to redirect the user to the corresponding activity, please use the following lines of code:

String uid = FirebaseAuth.getInstance().getCurrentUser().getUid();
usersRef.document(uid).get().addOnCompleteListener(new OnCompleteListener<DocumentSnapshot>() {
    @Override
    public void onComplete(@NonNull Task<DocumentSnapshot> task) {
        if (task.isSuccessful()) {
            DocumentSnapshot document = task.getResult();
            if (document.exists()) {
                String type = document.getString("type");
                if(type.equals("student")) {
                    startActivity(new Intent(MainActivity.this, Student.class));
                } else if (type.equals("teacher")) {
                    startActivity(new Intent(MainActivity.this, Teacher.class));
                }
            }
        }
    }
});