Real antinutrients are only in certain foods and usually foods you would need to refine and cook to eat. They're mainly in certain bitter leaves and legumes.
Fruits of any kind are safe foods and nuts too as many healthy hunter-gatherer societies who base their diet on nuts as staple have never suffered from the effect on antinutrients, actually as I said those are the population with the lowest rate of osteoporosis and those antinutrients mainly bind to mineral preventing the body from absorbing them. There are studies that prove how high intake of almonds and legumes prevent absoption of mineral. But none that show that a normal consuption of other varieties of nuts and fruits could cause these problem, actually evidence says otherwise as those population who live on a diet rich in plant food have also the highest level of minerals or the lowest incidence of mineral deficiencies diseases.
If plant foods are suspect as you say then it should be the meat you eat since those animals are eating the same modern plants, from the same soil .. when they do.
Who found phytochemicals in animal fat? Just asking

phytochemicals are not that evasive, each of them has a name and a function even if of course not all of them are known or will ever be known.
Since we're clearly suited to plant food consumption as we have characteristics of herbivorous animals other than characteristics of carnivorous animals I think is also wiser to consume them knowing we were meant to than guessing whether certain classes of food contain all we need, you may do this with the nutrients we know, what about the who knows how many nutrients we don't know and may never find out?

David