Create a JavaScript web resource with following functions.
function AttachHideEvent()
{
document.getElementById("crmGrid_SavedNewQuerySelector").setAttribute('onclick','HideItems();');
$( "#crmGrid_SavedNewQuerySelector" ).mouseout(function() { HideItems(); });
}
function HideItems()
{
if(document.getElementById("ViewSelector_fax")
!=null)
{
//fax
document.getElementById("ViewSelector_fax").style.visibility = "hidden";
document.getElementById("ViewSelector_fax").style.height="0px";
document.getElementById("ViewSelector_fax").style.float="left";
//Letter
document.getElementById("ViewSelector_letter").style.visibility = "hidden";
document.getElementById("ViewSelector_letter").style.height="0px";
document.getElementById("ViewSelector_letter").style.float="left";
}
}
Then add a enable rule to first button on activities homepage
ribbon and call this function with default value = true/ function name= AttachHideEvent/
webresource=web resource created.
In 2nd function add activities you want to hide from
dropdown.