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Get list of related objects whose type is in array of types
public abstract class WebObject : IValidatableObject
{
    public WebObject()
    {
        this.Id = Guid.NewGuid();
        RelatedTags = new List<Tag>();
        RelatedWebObjects = new List<WebObject>();
    }

    [Key, DatabaseGenerated(DatabaseGeneratedOption.None)]
    public Guid Id { get; set; }
    public virtual ICollection<WebObject> RelatedWebObjects { get; set; }
    public IList<Guid> RelatedWebObjectIds { get; set; }
}

public JsonResult GetRelatedWebObjectsByWebObject(Guid id, string relatedWebObjectTypes)
{
    JsonResult result = new JsonResult();
    Guid webSiteId = db.WebObjects.Find(id).WebSiteId;
    string[] relatedTypes = relatedWebObjectTypes.Split(',');
    var resultData = (from w in db.WebObjects
                      where w.Id == id
                      from rw in w.RelatedWebObjects
                      where rw.GetType().Name.Contains(relatedTypes)
                      select rw.Id).ToList();

    result.Data = resultData;
    result.JsonRequestBehavior = JsonRequestBehavior.AllowGet;
    return result;
}

var relatedTypes = new HashSet<string>(relatedWebObjectTypes);
var resultData = (from w in db.WebObjects
                  where w.Id == id
                    &&  relatedTypes.SetEquals
                          (w.RelatedWebObjects.Select(rwo => rwo.GetType().Name))

                  select w.RelatedWebObjectIds).ToList();

from w in db.WebObjects
where w.Id == id
from rw in w.RelatedWebObjects
where relatedWebObjectTypes.Contains(rw.GetType().Name)
select rw.Id

public JsonResult GetRelatedWebObjectsByWebObject(Guid id, string relatedWebObjectTypes)
    {
        JsonResult result = new JsonResult();
        Guid webSiteId = db.WebObjects.Find(id).WebSiteId;

        List<string> relatedTypes = new List<string>(relatedWebObjectTypes.Split(','));
        var resultData = (from w in db.WebObjects
                          where w.Id == id
                          from rw in w.RelatedWebObjects
                          select rw).ToList();

        result.Data = resultData.Where(w => relatedTypes.Contains(w.GetType().BaseType.Name) == true).Select(w => new { Id = w.Id, Type = w.GetType().BaseType.Name }).ToList();//w.Id).Select(w => w.GetType().BaseType.Name).ToList();
        result.JsonRequestBehavior = JsonRequestBehavior.AllowGet;
        return result;
    }