There are a few aspects to consider, but will always boil down to "you have to ask the individual".
Making a piece of cookware "safe" for a given person involves two components:
- Removing the contaminant in question in a manner that will prevent accidental ingestion of said contaminant.
- Making the item seem un-contaminated. At first glance this is similar to the first part, but has less to do with the physical molecules, and more to do with people's perception of cleanliness, as seen through their cultural lens. If a toothbrush falls on the bathroom floor, many people will throw it away because of the persistant sensation of uncleanliness, even if a dishwasher cycle would be more than enough to satisfy point 1. "Is it clean?" is as much about physics as it is about perception and intent.
For vegans and vegetarians, there are no guidelines of any kind. Individuals who are vegan or vegetarian for primarily environmental or health reasons will probably be satisfied with any simple cleaning to meet condition 1, and are probably unconcerned with item 2, as it applies to meat. Vegans and vegetarians who are primarily motivated by ethics will be more impacted by item 2, and may prefer not to eat off the pan. While some may be satisfied by various "rituals", there is no standard for such rituals.
For people who keep Kosher, some sects of Judaism allow for "kashering", which is the process of making something previously un-Kosher into something Kosher. Kashering is partially about item 1, but is primarily about item 2 - in some cases the cleaning is highly ritualized. Note that while there are some common themes to kashering, different sects will see the acts very differently, and may or may not "allow" certain methods for their followers.
For some appliances the process is fairly easy - a stainless steel sink can be Kashered with boiling water. Porcelain is seen as porous, and in many cases cannot be kashered (exceptions can be made for valuable old items, but they must remain unused for over a year). Ovens and oven-safe cooking items can be put through a self-cleaning cycle (around 800F), and must be thoroughly cleaned of all debris. Cast iron pans and other fry pans must have their entire seasoned coating removed, abrasively and/or through extremely high heat. The bare pan may then be re-seasoned in a proper way. Many consider that to be too extreme to be worth the time, and simple replacement of the cast iron cookware is advised.
Some examples of Kashering processes, though various sub-communities will see these items differently:
Ultimately, everyone will fall into a different place on the Item 1/Item 2 scale, and their habits or religion alone may not allow you to easily predict their reaction. In some cases, Jews determine that being an ungrateful guest is a greater sin than eating from a non-Kosher pan. Some vegans may find the pan forever unclean, but many will also take a more practical attitude when eating with friends than they would with their own cookware.
The best you can do is to take a good guess at whether someone is an Item 1 or and Item 2 prioritizer, and act accordingly. People who highly prioritize Item 2 will probably never be OK with your cast iron pan. People who prioritize Item 1 will probably be satisfied with any solid cleaning such as a heavy salt scrub with very hot water, and a re-oiled surface with an acceptable variety of oil.
In a world where wider groups of cultures are finding themselves in the same place, and individuals are thinking more about their own diets and making a broader range of food choices, it is becoming more acceptable to just ask. You should be able to ask someone, "Would you mind if this pan had been used to prepare meat in the past?" and not have them be offended, or yourself be offended at their answer (if they say "yes, I do mind"). I have so many friends with different dietary choices and traditions that I'm used to asking in dinner invites, "What is everyone's dietary situation right now?" No one is offended by the question, and their honest answers make it easy (and fun) to put together a meal that everyone will enjoy.