No more than people with shoes do. In fact, even after wiping their feet off on a mat before entering, a barefooter is far less likely to deposit nasty things on the floor indoors. Here's why:

Most people shower daily, which includes cleaning their feet. Therefore, any nasties that are deposited on a floor will only be from that one day.

In comparison, most people who wear shoes rarely clean them. Because of that, anything that's deposited from the shoes to a floor could be a culmination of stuff picked up by the shoes over the last several days, weeks, months or years.