I have a flutter app, I previously deployed, which I added firebase even though I didn't use their database. Now, I have another project that does not use firebase. My question is:
Is it a must to use firebase when deploying a flutter app even though I am using firebase in my code?
There is no (explicit or implicit) requirement to use Firebase for your Flutter app. And even when you use Firebase, you don't have to use all of its (18 or so) products.
You can use parts of Firebase that you like, and use alternative products that you prefer for other parts.
For example, it is quite common for (Flutter) web apps to use Firebase Authentication to sign users in, and then use one of the databases in Firebase (Firestore or Realtime Database) to store data, but then deploy the web app to a non-Firebase hosting provider.
It's also quite common for (Flutter) web apps to use Firebase Cloud Messaging to deliver push notifications and background data messages, but no other parts of Firebase.
