It depends on what the issue is and what habesha muslim you're talking about, since at least half of ethiopia's 110 million population is Muslim, so you have diverse beliefs and perspectives.
if the issue is related to Ethiopia, people naturally side with their country, but I do remember seeing protests in Ethiopia against the invasion of Somalia (but remember, the average Ethiopian is pretty much helpless in regards to what decisions the govt makes), and I do remember the govt getting backlash for supporting the invasion of Iraq by the West, from habesha/ethio Muslims.