I understand that animals are naturally scared of humans because we basically slaughtered every living thing we found in our way for millennia. How long does it take for them to genetically 'forget' we are a threat?
Perhaps counter-intuitively, fear of humans is often a learned behaviour. There are accounts, such as one made by Charles Darwin following his visit to the Galapagos islands;
Birds born and bred in proximity to humans will have learned that we are actually to be avoided.
Ducks and swans, for instance, (and this is quite anecdotal) live in very close proximity to a lot of humans in cities, and feel confident walking picking up food. However if you try to get close to one they are very quick to get out of the way. The only exceptions to this are learned behaviours, such as when someone stands and feeds them.
In the wild animals may be cautious of humans if we are much bigger than them, but if they have no experience at all of human contact they may just ignore them. This quite often happens with film crews in Antarctica, as in the below image from the BBC's Frozen Planet series.