This solution has been tested on JIRA 7.1.4, and Jira 8.5.0

• Add the following JavaScript to the Announcement Banner NOTE: This will remove the option from filters AND dashboards.

  <script type='text/javascript'>
  AJS.toInit(function()
  {   
      var urlPath = $(location).attr('pathname');
      console.log(urlPath);
      if (urlPath.toLowerCase().indexOf("editportalpage") >= 0 || urlPath.toLowerCase().indexOf("editfilter")  >= 0 || urlPath.toLowerCase().indexOf("addportalpage")  >= 0) {
          
          AJS.$("#share_type_selector_viewers option[value='global']").remove();
  		AJS.$("#share_type_selector option[value='global']").remove();
      }
  });
  
  </script>

  
  

An alternative method is to rely on CSS instead of Javascript. This will work regardless of race-conditions on the browser page load but is more sensitive to version updates. These have been validated on Jira 9.4 and 9.11.

They are described in these two Issues:

JRASERVER-65962 - Getting issue details... STATUS

<!-- Custom CSS to hide the "Logged in users" option when sharing Filters and Dashboards (JRASERVER-65962) -->
<style>
#share_type_selector_viewers > option[value="loggedin"] {
  display: none !important;
}
</style>

JRASERVER-69095 - Getting issue details... STATUS

<!-- Custom CSS to hide the "Shared" option on Users profile (JRASERVER-69095) -->
<style>
#update-user-preferences #update-user-preferences-sharing option:nth-child(1) {
  display: none !important;
}
</style>

 This solution has been tested on JIRA 5.1 and on JIRA 6.3.

Hiding the option 'Everyone' by customizing the edit-share-types.jsp template:

1. Shutdown JIRA.
2. Open the edit-share-types.jsp located in the JIRA-INSTALL/atlassian-jira/template/aui directory.
   Make a backup of this file.

3. Modify the file from:

   edit-share-types.jsp

                       <select id="share_type_selector">
                           <ww:iterator value=".">
                               <option value="<ww:property value="./shareType"/>"><ww:property value="./shareTypeLabel"/></option>
                           </ww:iterator>
                       </select>
                       <ww:iterator value="." status="'typeStatus'">
                           <span id="share_<ww:property value="./shareType"/>" <ww:if test="@typeStatus/first == false">style="display:none"</ww:if>>
                               <ww:property value="./shareTypeEditor" escape="false"/>
                               <ww:if test="./addButtonNeeded == true">
                                   <span class="addShare" id="share_add_<ww:property value="./shareType"/>"><img src="<%= request.getContextPath() %>/images/icons/16add_blue.png" />
                                   <ww:text name="'common.sharing.add.share'"/></span>
                               </ww:if>
                           </span>
                       </ww:iterator>
   

   To:

   edit-share-types.jsp

                       <select id="share_type_selector">
                           <ww:iterator value=".">
                               <ww:if test="./shareTypeLabel != 'Everyone'">
                                   <option value="<ww:property value="./shareType"/>"><ww:property value="./shareTypeLabel"/></option>
                               </ww:if>
                           </ww:iterator>
                       </select>
                       <ww:iterator value="." status="'typeStatus'">
                           <span id="share_<ww:property value="./shareType"/>" <ww:if test="@typeStatus/first == false">style="display:none"</ww:if>>
                               <ww:property value="./shareTypeEditor" escape="false"/>
                                   <ww:if test="./shareTypeLabel != 'Everyone'">
                                       <ww:if test="./addButtonNeeded == true">
                                           <span class="addShare" id="share_add_<ww:property value="./shareType"/>"><img src="<%= request.getContextPath() %>/images/icons/16add_blue.png" />
                                           <ww:text name="'common.sharing.add.share'"/></span>
                                       </ww:if>
                                   </ww:if>
                           </span>
                       </ww:iterator>

4. Delete the contents of the JIRA-INSTALL/work folder.

5. Restart JIRA.