If you have a different role per site, you can use this to restrict who can see each block. 

Blocks can have an Access attribute like so:

[ContentType(DisplayName = "Test Block", GUID = "xxxx-xxxx")]
[Access(Roles = "SiteBRole")]
public class TestBlock : BlockData {
}

This'll filter out the block for everyone not in the SiteBRole.

If you want to filter it per site, you can implement a ContentTypeAvailabilityService  as suggested here.
It'll allow you to filter the list of pages and blocks per your own criteria.

This can be done but you need to write a validator for the XhtmlString type (in combination with Arjan Paauw's answer).

Here's a brilliant blog post on it, https://surjitbharath.wordpress.com/2017/02/02/episerver-10-restrict-any-block-types-on-xhtmlstring-property-using-the-validation-attribute/

Codesnippet from Surjit's Dev Blog

Property

[Display(Name = "Text", GroupName = SystemTabNames.Content)]
[XHtmlStringAllowedBlockTypes(new[] { typeof(TextBlock), typeof(ImageBlock) })]
public virtual XhtmlString RichText { get; set; }

Attribute

public class XHtmlStringAllowedBlockTypes: ValidationAttribute {
  private readonly Type[] allowedTypes;
  public XHtmlStringAllowedBlockTypes(Type[] allowedTypes) {
    this.allowedTypes = allowedTypes;
  }

  protected override ValidationResult IsValid(object value, ValidationContext context) {
    var contentData = context.ObjectInstance as IContentData;

    if (contentData != null && contentData.Property[context.MemberName].Value is XhtmlString) {
      var richTextProperty = (XhtmlString) contentData.Property[context.MemberName].Value;

      foreach(ContentFragment fragment in richTextProperty.Fragments.Where(x => x is ContentFragment)) {
        var content = ServiceLocator.Current.GetInstance < IContentRepository > ().Get < IContentData > (fragment.ContentLink);

        foreach(var allowedType in allowedTypes) {
          if (allowedType.IsInstanceOfType(content)) {
            return new ValidationResult(string.Format("You cannot add {0} to {1}", content.GetType(), context.MemberName));
          }
        }
      }
    }

    return ValidationResult.Success;
  }
}

Thanks for the advice guys. I implemented a ContentTypeAvailabilityService  that did the trick for me :)