When was this time that online payments were done with money orders? Some of the earliest online merchants that were associated with AOL and Prodigy accepted credit cards. Amazon definitely accepted credit cards from day one.
In the mid to late 90s many retailers online operated like mail-order catalogs with catalogs delivered via http. Many of them were mail-order businesses first, and so they accepted payments for online purchases the same way they did for their majority of their customers.
This was also normal for eBay payments at the time.
There were, of course, a few that did accept credit cards, but many people were weary about using those features because very little of the web used HTTPS at the time. Even Amazon accepted money orders (and personal checks!) for this reason.