It's happened many times that a certain food rose to popularity as a "health food" only to later fall from that status when we learned more about how the food is produced or a negative effect it has on the body.
Remember when "whole wheat" was considered a health food? Now we know wheat creates holes in your gut lining and triggers systemic inflammation.
Or soy, which seemingly every "healthy" person had in their fridge 10 years ago. Soy milk has been largely replaced by almond milk over the past 10 years - in large part because it's now widely known that natural chemicals in soy have estrogen-like effects and soy is particularly susceptible to contamination by mold toxins.
Well, there's now a new wave of "healthy" foods coming under scrutiny. The issue this time around is natural plant toxins.
What Are Plant Toxins?
Plant toxins are natural compounds produced by a huge number of plants, including many we grow as crops. In most cases, these toxins are defense mechanisms the plant produces to protect itself against being overeaten by insects in its environment.
If an insect eats enough of a one of these plants, the toxic chemicals would accumulate in the insect to a level where cell and tissue function are disrupted and the insect dies. In this way, plant toxins play an important role in nature's checks-and-balances system.
We now know that these same plant toxins that disrupt cell function in insects can potentially have the same effect in our own bodies. Unless you're eating half your body weight in plant-matter in a single meal the way an insect might, plant toxins aren't going to kill you, but over time they certainly can have a significant impact of several of our body's systems.
So how much (or how little) do we need to worry about these natural toxins in our food? Depends on what you're eating.
First, let's cover the 4 main types of plant toxins, how they each affect the body and which foods contain these toxins in levels significant enough to warrant concern.
WHAT PHYTATES DO: Phytates bind to minerals in your gut, preventing them from being absorbed by your body. Suppression of iron absorption by phytates is what tends to get the most attention, but zinc, calcium and phosphorus are also affected.  A recent study has even suggested that diets heavy in phytates are responsible for the widespread zinc deficiencies seen commonly in the developing world. 
WHICH FOODS?: Beans, grains, seeds and legumes. Beans are the biggest concern.
CAN PHYTATES BE REMOVED?: Soaking, sprouting and fermenting all reduce phytate levels, but do not eliminate them.
WHAT LECTINS DO: Lectins disrupt the functioning of the epithelium, the oh-so-critical thin layer of cells lining your gut that keeps undigested food from slipping into your bloodstream. Over time, lectins in the diet will actually create holes in the epithelium, referred to as "leaky gut syndrome". 
When the epithelium is compromised, incompletely-digested particles from your food can slip into your bloodstream. Your body treats these food particles as a threat and triggers an immune response that creates systemic inflammation. This is a similar mechanism to how wheat gluten creates holes in the epithelium.
Lectins have also been shown to disrupt gut bacteria function, which given how critical these bacteria are to our well-being, is a major concern as well.
WHICH FOODS?: Beans and grains again. Soy beans and kidney beans are the biggest concerns.
CAN LECTINS BE REMOVED?: Cooking and fermenting reduce lectins, but do not remove them.
WHAT SAPONINS DO: Saponins actually have a soap-like foaming property when they're added to liquid. In part because of this property, saponins disrupt epithelial function and create other digestive issues. Saponins have also been connected to damaging red blood cells, inhibiting enzymes and interfering with thyroid function. 
WHICH FOODS? Soy beans, chick peas, oats and quinoa. We've recently learned that quinoa has particularly high levels of saponins, making it a real concern.
CAN SAPONINS BE REMOVED?: Not really. Cooking doesn't have much of an impact, nor does sprouting or fermentation. Saponins can be removed via alcohol extraction, but this obviously isn't a practical technique.
WHAT OXALATES DO: Oxalates interfere with calcium absorption.  Oxalates will also crystalize in tissues if consumed regularly, creating arthritis-like symptoms and even kidney stones.
WHICH FOODS?: Kale. Spinach, chard, other hearty leafy greens.
CAN OXALATES BE REMOVED?: Cooking will slightly reduce levels of oxalates. You can also take a calcium/magnesium supplement with these foods. Calcium and magnesium bind to the oxalates in your stomach and prevent them from being absorbed.
How Worried Should You Be?
What all of these plant toxins have in common is that they only have significant negative impacts if they are allowed to accumulate in the body.
Eating quinoa or beans or kale once a week realistically won't have a negative impact. Our bodies are pretty good at clearing out toxins, including plant toxins, when given enough time.
If these foods are a regular part of your diet, however, plant toxins can be a major concern. If you're eating any of the foods listed above more than once or twice a week, it would be wise to find substitute that doesn't have plant toxin issues.
Which Foods Are The Most Problematic?
Soy appears all over the list above. If the phytoestrogen and mold-toxin issues weren't enough, the high levels of plant-toxins in soy should be enough to convince you to remove it from your diet.
Quinoa appears to be a particularly potent source of saponins, so consuming it with any regularity puts you at risk for gastrointestinal issues.
Grains, beans and legumes also appear all over the list. With grains, plant toxins are perhaps the least of your worries, as mold contamination is realistically a much bigger issue.
If you're a kale addict (I'm certainly one), and the idea of cutting back on kale sounds like torture, don't panic. In addition to taking a calcium supplement with your kale, you can also "cycle" your greens to avoid accumulation of oxalates.
Taking 5-7 consecutive days out of the month to remove kale (or spinach, chard, etc) from your diet and replace it with another oxalate-free green will allow your body to clear out any oxalates that have accumulated. Lettuce, arugula and other "mixed greens" are good low-oxalate or oxalate-free greens.