Switching away from meat will certainly help to address the development of resistant microbes, but if you can make a switch instead to meat that was raised with regenerative pasture management practices, you can additionally have a large positive impact on many other environmental factors. Look for terms like "high-density grazing," "holistic grazing," "holistic management," or "management-intensive grazing (MIG)."
This TED talk [1] covers some of the information, for more you can google around for the above terms (sorry I don't have a good link handy). Correctly managing grazing livestock can actually reverse desertification and trap tons of carbon per year per acre in the soil. Of course, doing it wrong can have the opposite effect, so if you go this route it's important to know whether your farmer is running his operation with land restoration in mind.
Conventional vegetable production also comes with a slew of its own problems (breeding of herbicide-resistant weeds [2] being something closely related to the topic at hand). Eating in a way that doesn't cause harm is a tricky thing these days.
[1] - http://www.ted.com/talks/allan_savory_how_to_green_the_world...
[2] - http://www.sciencedaily.com/releases/2012/10/121002092839.ht...
*edited for formatting