In my experience, one can't get the same reading experience as with eInk due to the light intensity being so different on backlit devices (even with the lighting dialled down), but pretty much every reader application that I've tried on both my iPad and Android smartphone do offer some font/background selections.
Some ebook shop apps (Kindle and Kobo among them) offer only a very basic selection (black on white, black on sepia, white on black) - with those, if I use a backlit reader, I prefer black text on sepia background. Others offer full customisation (I'm fairly sure Aldiko does on Android), so you can choose whatever font/background combination you're most comfortable with, e.g. black text on off-white/grey background to get it to look more like eInk.
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