HAVE TO? No. It is bad to do so? Also No.
The biggest issue for static build up is humidity. If you have low humidity when building, you will have more static issues. Most components. if handled by the edges are fairly static tolerant. Installing the CPU into the motherboard is the most static sensitive part of building a PC.
Sure, you wouldn't want to kill your $300 CPU by not wearing a $3 anti-static band.
There are gloves that cost $1 a pair too.
If you are in a hurry and you don't want to wait for the anti-static gloves, you can process with your bare hands, but be very careful, you should wear simple clothes, avoid clothes made with wool, fur, polyester and silk. Find some large metal object like water pipe, computer case, touch it firmly with both hands from time to time to discharge possible static electricity from your body.
No. You can work barefoot on hardwood or tiled floor and touch the metal part of a case every now and then if you feel unsure, but once you discharge once and you don't move away from your working area, you don't need to constantly discharge, as long as you're not working on carpets.