We still hear about shoppers who are afraid of online shopping because of security concerns. Some of this fear is fed by prominent stories in the media about identity theft, credit card fraud and phishing. many of the fears are overblown.
The fact is, online shopping is safer than ever before. Website security is well established. Payment card companies have adopted new and better means of authentication. Encryption techniques are commonly used and with modern systems and browsers, need not slow down transactions.
True, shoppers still need to be aware of the danger of fraud, fake sites, and phishing and hacking. However, many people these days have the basic level of "web smarts" to be able to tell when something is not right..
Online shopping has been a growing industry. Each year sees significant increases in the volume and this year it is likely to grow again. Hopefully the numbers of people who are deterred by security concerns is diminishing. Here's an article on this topic with more detail.