The Protected Mode is designed to block ActiveX from loading through the browser. The ALM client is designed in ActiveX and therefore would need to allow it to run (this is why you see the error).
If your users have local admin rights, they can right click on the Internet Explorer icon and choose ''Run as Administrator''. Doing so will bypass the Protected Mode and allow the ActiveX and ALM client to load. If your users are not local admin nor you are unable to get an exception from the security policy then ALM will not be able to load through the Internet Explorer browser.
Alternately, you may still be able to run ALM using the ''HP ALM Explorer''. This is an Add-in utility that you may download from the ALM Add-Ins / Utilities page. This Add-in installs on the client machines and provides a browser like interface. However, it does not take it's security settings from Internet Explorer, so you can still load ALM through the utility even when protected mode is enabled.