I've been a fan of anime for over 18 years now, having seen a good number of anime franchises and notable titles both past and present as I've seen just over 2000 anime titles. My biggest turn offs with anime titles are fan service heavy titles, moe pandering and the use of gratuitous violence and sex for shock value in an anime title. Feel free to dig into my list to see any anime I've dabbled into over the years to find anything of interest.
Don't be too surprised if I have a slim list for manga as I am more a viewer of anime than I am a reader of manga. I hardly read manga nowadays except in cases where I need to look through it to recall events from what I read from the past, though I may make an exception if I come across a manga title that has yet to be adapted into anime form.