I am also having the same problem entering new contacts after upgrading to High Sierra. After a bunch of testing, here is what is happening very consistently:
1. Type Command+N to create a new contact. A contact called "No name" appears in the contact list and the cursor is in the "First" name field. Do nothing else. Wait 22-25 seconds and the area for entering the new contact refreshes to display "No card". The "No name" contact has been saved.
2. I can repeat number one but enter content in any of the fields and if I haven't saved the contact within about 22-25 seconds I get the same result as #1.
3. If I create and save a contact within 22-25 seconds it will appear in the contacts list to the left. However, it will disappear from the list a great deal of the time at the 22-25 second mark after having started the new contact. The "No name" contact will then stay in the contact list.
4. If I create and save a contact within 22-25 seconds as in #3 above, the chances of it being saved permanently is increased the faster I save. For example, if I save the contact within 5-10 seconds it often saves the new contact permanently, but not always. If I save the contact within 15-22 seconds after creating it, it usually doesn't save permanently but once in a while it will.
5. If I disable the Google account being synced by going to Contacts preferences>Accounts> and deselecting the "Enable this account" checkbox, none of the issues above present themselves.
6. The issues are repeatable after restarting, in Safe Boot mode, and after disabling/reenabling the synced Google account under Contacts preferences.
It seems pretty clear that Contacts is trying to sync with Google approximately every 22-25 seconds and something about the sync is going wrong and deleting new contacts most of the time.