The primary thing that made my father feel he had to, despite religion, accept evolution is pretty simple, the fact that we have so much in common with other mammals. I grew up with that attitude because there were many relatives who felt the same empathy with mammals and essentially came to the same conclusion. This of course means we are not 'special' but rather a part of the mammalian order.
To point out a few, mammals (except in some cases of monotremes) think, have emotions, plan, feel pleasure and pain, have sex (similarly), crap (the same), piss (the same), have hair, give live birth, females provide milk, train their offspring, etc. etc,
Because the old man's emotional connection with other mammals was so pronounced, he even felt that horses, cats, dogs, etc. went to heaven like people.
Once one gets over the 'humans as special' dogma, those primates, especially apes, start looking and even behaving a lot like people. It becomes no great leap to see the connection especially after being exposed to the findings of physical anthropology and the obvious intermediate forms between humans and the common ancestor of all apes.
After that, the ToE becomes a given.
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