So what is the position of the Zone Diet on consumption of phytates and foods containing phytic acid, i.e. grains, beans, soy products, nuts, etc.? It seems those followers of Weston Price, Dr. Mercola and the Paleo Diet seem to have a negative view on the use of grains, legumes and excessive consumption of nuts. This really seems to cut into the intake of what by many are considered healthy foods, and drastically limits options. Other studies seem to tout the cancer fighting properties of phytates.

Dr. Sears lists a few as favorable, but most are not favorable,
so the Zone is mostly Paleo.
Steel Cut Oats and black beans, and I think rd kidney beans are the only grains/legumes I can recall that Dr. Sears considers favorable,
and Paleo avoids or severely restricts.
Some nuts are encouraged, others are not, just like Paleo, it depends on their Omega-6 content.
Following the Zone is mostly Vegetables, some fruits - very similar to Paleo.
The major difference is that Paleo encourages up to 50% in fat, and fewer Carbs than the
30-40-30 prescribed as a starting point in the Zone.
And Paleo folks & Dr. Mercola encourage Coconut Oil, while Dr. Sears advise in moderation.
Otherwise the two are very, very close, including other aspects.

Grains, esp Gluten containing grains, mostly wheat, is not the same wheat prior to 1950's/60's.
It was hybrid/changed to increase yield. Changed the gluten, and thus all of the "anti-nutrients"
and now increased gluten sensitivity and Celiac disease we see becoming more and more prevalent.
That's why Palep, Mercola, etc. is not for grains. (See Mark Sisson Daily Apple web pages on anti-nutrients in grains.)
And Dr. Sears is not for grains because they do not have a positive effect on blood sugar, and one of main principles of Zone is keeping internal
(silent) inflammation down. One way Zone does that is keeping the blood sugar stable. And another is reversing the Omega-6/Omega-3 ratio back to
what God/Nature intended - which as reversed over the decades based on our processed food intake. Whole, raw, natural vegetables is also acceptable
in the Zone, though not necessary. And meats/fish should be Pastured/wild and not grain-fed/farmed.
Plus, now a days in addition to meats being grain=fed, hormone and ant-biotic shot-up - now 90% of
corn/corn products (which are fed to our food supply animals) are GMO!

Lentils and barley are also favorable foods for the Zone Diet.

Thanks. Ok then, what might be an advisable guideline for weekly or daily consumption of grains, beans and nuts before they might be considered compromising to one's well being?

Paleo doesn't always allow coconut oil. Phytates disrupt the absorption of many minerals. I'm glad to be done with them, except I still eat nuts. Wondering why Sears is ok with almonds and pistachios when both have poor omega-6 to omega-3 ratio.

It's because the fat in almonds and pistachios is predominately monounsaturated.