Restrict which types of an Enum can be selected in inspector.

This might be old but it still might be helpful for somebody. Use InspectorName attribute with empty string:

 enum MyEnum
 {
   [InspectorName(null)]
   HiddenValue,

   Value1,

   Value2
 }

Just ressurecting the post in case of someone needs: I've made a slightly different approach.

First, I've created a custom enum with the values I wanted to show.

Then, each value of my custom enum receites the value of the Unity Enum type I want to set. Then, I only need to cast to the Unity Enum Type to set the value to object.

See the example with an Input Field

 //That's my custom enum. Only exposes 2 types of numeric values
 public enum CustomInputType
     {
         Integer = InputField.ContentType.IntegerNumber,
         Decimal = InputField.ContentType.DecimalNumber
     }
 
 //That's the cast I do to set the content type on my InputField
 this.inputField.contentType = (InputField.ContentType) this.CustomInputType;

I would look into creating a custom property drawer that ignores specified values.

Why not create 2 Enum, one public that only have the values you want exposed in the inspector, and another one private that you use in your script. At Start() you can changes the private version based what is in the public instance with IF statements.

Use the attribute [UnityEngine.HideInInspector] above the entry of your enum you want to hide. ,Use the attribute [UnityEngine.HideInInspector] above the entry you want to hide.