You can eat meat quite healthily, providing you buy organic or, for beef and lamb, Pasture for Life certified meat.
The Pasture for life system means that animals eat only grass and forage crops for their entire life. Usually all grown on the same farm they spend al their lives on and where the animals tread their manure intothe ground, feeding the grass and flowers that grow in it, enhancing diversity and reducing emissions.
It is, of course expensive, but I have just halved the size of the portion of meat I use. Now 1lb of beef, in a casserole with lots of vegetables is sufficient to feed 8. and th eprice is back comparable with supermarket meat.