I will eat labeled, USDA stamped beef, pork, or chicken. I will not eat "mystery meat". Not only do I worry about the "yuck" factor, but also about disease such as trichinosis from dogs and rats, not to mention bubonic plague from cats and rats. I will rapidly go on a vegetarian diet if I can't identify my food source.
I'm sorry, but I can't resist
You might want to seriously consider not leaving the U.S.A or at least staying in North America (and avoid ordering "meat" off of a menu and inspect the "side of beef" before they start to cut it up for you to buy at the store since you're unlikely to (rarely) see the USDA stamp on anything after it's been cut up for sale).
I suppose you might be able to manage the vegetarian diet in some countries you could visit, but that's not always easy (in some places you won't enjoy your "new diet" much when eating out. Being rather limited in what's available for you to eat unless you rent a house so you can buy and prepare all your food)
In most of the world (including the US) when you go to a place to eat you don't get to inspect the meat (see comment above for checking the USDA stamp and you'd be hard pressed to tell what cut piece of meat came from anyway). You order a dish off the menu (or in some places you point to what you want like the pot of stew or the whatever else might have been prepared that day for customers to select from). In any eating establishment anywhere in the world you are going on "faith" that you're getting what you ordered (basically "mystery meat" in most cases since you can't usually positively know what it came from). Unless of course it's one of the places (and you order something small) where they bring the entire fish, rabbit, etc..... (head and all). Then you have excellent odds of knowing almost exactly what you got (providing of course that you're familiar with what it would look like in it's skinless and cooked state..... e.g. squirrels have an uncanny resemblance to rats once the skin and tales are removed, but then their almost 1st cousins)
Oh, and trichinosis is a greater concern with pork than with canine
.....unless you only eat US factory raised pork in which case they've almost eliminated it, but with grazing, free range "healthier" pork you still run a risk of it unless you cook it properly. But then cooking something properly is how we make poultry and eggs safe to eat too. The need to prepare/cook food properly to avoid a health risk is not just restricted to one or two species of animal.
And be careful with the vegetarian diets. Make sure you take your supplements (e.g. remember we all must have B-12....not to mention the human body has difficult time processing omega 3 from vegetable sources and can't get as much as we really need except from animal sources which we can process very efficiently) and look out for contamination (people die for that too).