I dont think that the sight is supposed to come with plastic inserts. What makes you believe that they do? I cant say I know everyhing about this particular flip up fron sight, but if it is made to fit milspec rails, and the rails on your armalite gas tube are milspec rails, they should work together.
Just to be sure, maybe try to mount the BM front sight to one of the flat top rails. They should be in spec. If the front sight does not secure to that rail, there is probably something wrong going on with the sight. If it does fit, then something is probably wrong with the front sight rail on your barrel.
BTW, all of this is purely guess work. I have never seen the Bushmaster flip up front sight you are talking about in person, but looked at it on their www site. Sorry I could not be of more help?