Safety is relative! Some of us will take risks that others would never contemplate.
When 767s first started crossing the Atlantic non stop I was invited to Kansas City by TWA. The proposed route was via St Louis on the 767. I asked nicely if we could please go via Chicago on the 747 and they kindly said yes; at that point the whole idea of twins over water was far to new for me to accept. Stupid? Possibly. The reason was that, at the time, the whole issue was still being discussed in magazines like Flight International and I wasn't comfortable.
These days I have what I think is a more rounded(?) approach. There are airlines that I will avoid if possible. I will take a non stop over a stop/change if possible (why expose myself to the riskiest parts of a flight more than I have to?). I will fly airlines that I would otherwise avoid if I'm "in country" and the alternative is a bus or car journey where the accident rate is high. I will fly on twins over water. At the moment I would try and avoid booking a 787 because I'm not comfortable that simply containing the batteries is a solution.
(But here is an interesting conundrum I'm currently thinking about going to Madagascar. The tour I've looked at uses Air France to get there. They will sell me the ground arrangements and allow me to book my own flights so Air Madagascar enters the options. Probably not, thank you, even though the tour includes one of their flights internally and I will use that on the basis that it is probably safer than a bus trip. Air France? Not the best safety record in recent years. The other alternative seems to be Kenya Airways and that's probably where I'll go if I decide to take the tour).
So what would I do if presented with a 787 at the gate when I thought I was going to be on something else? I'd like to think that with things like on-line checkin I would actually find out before I go to the airport, at least then I would have time to think about it. But, in the end I think I would board despite my reservations.
Like I said we all have our own ideas of safety and they aren't always rational.