Contadicting is saying the opposite; conflicting is fighting. People may have conflicting opinions but not be unfriendly towards each other. (Here, 'conflicting opinions' is a collocation; it simply means that the opinions are at odds with each other - not that the holders come to blows!)
'Although their ideas were not in tune with each other, and the two men sometimes contradicted each other, there was no risk that the contradiction might lead to conflict.'
(As one who has learnt Latin, I see no similarity between contra [=against] + dicere [=say] and confligere [=fight with]. But I can see that on the face of it the two words look similar - starting 'con-' and ending '-ict'. )