Using macOS without an Apple ID?

No, you do not absolutely need one.

It is mostly used for synchronizing with your other devices, which you’ve stated that you do not want anyways.

However it will still be most practical if you create a new Apple-ID to be used exclusively for that computer. If you do not, you’ll not be able to download software from the App Store.

Note that you do not have to enter that Apple-ID in any of the systems that would otherwise sync data. Your files, photos, calendars, mails, contacts, etc. will stay completely private and not synced with anything, even if you use an Apple-ID for purchasing or otherwise downloading software from Apple.

The problem is that I don't want to use my Mac with my AppleID because I am very afraid that it will sync with my other apple devices and I'm not a big fan of this at all.

You can turn off sync and iCloud which will stop devices syncing.

Do I really need an AppleID for macOS and which parts of macOS I cannot use without an AppleID

An Apple ID is heavily recommended. A lot of services will be disabled. You won’t be able to download any apps from the App Store or iTunes.

These are some of the most widely used services that you access with your Apple ID:

• App Store

• Apple Music

• Apple Online Store

• Apple Retail services and programs (Concierge, Joint Venture, workshops, and youth programs)

• Apple Store app

• Apple Support Communities

• FaceTime

• Find My Friends

• Find My iPhone

• Game Center

• Books Store

• iCloud

• iMessage

• iTunes Genius

• iTunes Home Sharing

• iTunes Match

• iTunes Store

• iTunes U

• Mac App Store

• Photo Print Products