I think it would be really hard if you were in a situation in which you feel that you and your child would be judged harshly and universally.
We live in a suburb of a large city. I'm sure I know kids conceived by DE and DS; in fact I know for sure I do as we know lots of families with same-sex parents. The area I live in has a lot of people who are very career-focused; hence older moms are not a strange thing. My DD (age 7, OE) knows lots and lots of twins. Some I know are DE and/or DS twins; some I suspect are based on mom's age (but honestly I never would have guessed anything if I weren't going through this right now).
My point is that one of the things that helped me come to terms with DE pretty quickly is that it appears to be common where I live. The kids I'm sure are DE are so very much their moms' kids - even the ones who don't look one bit like their mother.
I'm cycling right now, transfer to happen later this month. If we succeed, the plan so far is to tell the child from the beginning. Our families have no idea - we may tell them later. We want the child to know about his/her origins early on. We are less certain about when we will tell DD. She will be 8 when the baby is born (older if we don't succeed right away), and she can wrap her mind around some of these issues. If we tell one or both kids and they blurt it out to our family or friends or whomever, we will deal. That's one advantage of being a 40+ mom - I just don't care as much as I used to about what my family thinks
That's not to say it wouldn't hurt if my parents or my in-laws rejected the child, but it wouldn't change my choice to tell. And protect my child from family obnoxiousness! I hope this doesn't happen, but if it does, oh well.