My mother taught me to be polite and always hold the door for strangers. Those early lessons are hard to ignore, especially when the weather is bad. It is very hard to tell a coworker "no" and force them to walk around to the main entrance of the building in the rain or snow. Unfortunately, in today's world of identity theft, litigation and physical violence, those polite habits are increasingly a threat to the safety and security of our coworkers and customers. Imagine the risks if you let someone in who does not belong here. With unescorted access to our building, an intruder could pick up enough information to commit identity theft against our customers on a massive scale. Or worse, the intruder could be coming in with malicious intent toward a fellow employee.
Every company needs have a policy about visitors and needs to enforce a strict "no tailgating" policy. Visitors should always be signed in and out of your facility and should always be escorted while in any non-public part of your facility. If a customer or other important visitor comes to the wrong door, politely greet them and then tactfully escort them to the correct entrance so they can be signed in.
Employees and contractors should be required to show their authentication every time they enter the building. Do not hold the door for anyone and please do not expect someone to hold the door for you. This is an essential part of security discipline.
If someone does follow you into a non-public part of your building and/or refuses to show their ID badge, immediately go to the nearest phone and call your local Security contact. Give them your name, location and a description of the intruder. The borders between information security and physical security are increasingly blurry. These days, security is everyone's job.