These products may not have been tested on animals but often contain animal by-products among their ingredients. Look for products explicitly labeled as containing no animal ingredients. How you handle this is up to you. Some people may choose to bring their own food to various social functions. Others may prefer to try to work with the people providing the food in order to reach a suitable solution.
Caterers are usually happy to provide specialty foods as long as they are given advance notice.
Another good solution is to host social functions in order to preempt any possible food problems. Invite your family to your place for Thanksgiving, or volunteer to do the cooking. Your relatives will hopefully be willing to trade the meat for the convenience, and it provides a good platform to introduce others to vegan foods. The caveat I mentioned at the beginning of the primer about not getting too nuts about your lifestyle applies no more than here. Simply put, animal products are almost everywhere.