I am not sure left-handedness was particularly opposed by Islam as such.
The custom in Arab countries (and may be Muslim in general ) is that people eat with their right hand and wipe themselves after defecation with an object held in the left one. This is a smart hygienic precaution in an area with little water. Wasn't it Sir Richard Burton who almost lost his head while traveling to Mecca dressed like an Arab, but using the wrong hand?
Are there any specific anti-Southpaw

injunctions in Islam?
Western societies were not much different; many positive human qualities are connected with the right hand: righteousness, dexterity etc. And a malicious person is called sinister (left in Latin).