Yes, the estrogen a female mammal produces is 1000x stronger than the estrogen a plant produces.
Are your sources referring to plant estrogen (phytoestrogen). Or did they say it was actually estrogen (or estradiol). They are different: the plant estrogen being the weaker of the two. Some AG and beef industry articles will go on and on about phytoestrogens and never once mention the more concerning estradiol levels of their 'products'.
It is hypothesized that the 'real' estrogen (ie. animal estrogen), from meat and dairy is the cause of many cancers. Here is a study
in that regard.
Personally I would think 4 cups is a little too much of any one food. There are other good protein sources and to ensure you get all the micronutrients you need, you should really mix it up a bit. Hopefully you are including grains in your diet to complete the protein from legumes.