Can I share HBO Max subscription to someone (my wife) with a different Apple ID?

HBO Max does not depend on your Apple ID, and does not support Apple Family Sharing.

HBO Max allows up to 5 user profiles per HBO Max account, to share with family members/household members.

All about HBO Max - HBO Max Help Center

↳ Create multiple profiles

Streaming on too many devices - HBO Max Help Center

Users can sign in to the app at any of their devices, but multiple users can stream from one account on up to 3 devices at the same time.

Hello! It depends, here's is an article that can help you. Share Apple and App Store subscriptions with family members on iPhone – Apple Support (UK)

Share App Store subscriptions

You can choose which eligible App Store  subscriptions you share with family members. For information about the App Store, see Get apps in the App Store on iPhone.

1. Go to Settings  > [your name] > Subscriptions.
2. Do either of the following:

• • Share all new subscriptions: Turn on Share with Family. When you purchase a new subscription that’s eligible for sharing, it’s shared with your Family Sharing members by default.
• Change the settings of a specific subscription: Tap a subscription, then turn Share with Family on or off.
  • If you don’t see Share with Family, the subscription isn’t eligible for sharing.

Or you can just simple share your account password with your wife.