Some 100 leading consumer sites were assessed by web-testing firm SciVisum.
Websites that proved difficult for Firefox users to navigate included the government website Jobcentreplus.gov.uk and the cinema site Odeon.co.uk.
Firefox is an open source alternative to Microsoft's Internet Explorer and has proved popular since its launch in November last year.
While most people still use Microsoft's browser, Firefox is slowly making inroads.
Its share of the browser market grew to 8% in May, up from 5.59% at the beginning of the year, according to US-based analysts NetApplications.
Microsoft IE's share of the market dropped to 87.23% in May, compared to 90.31% in January.
Of the websites that SciVisum tested, 3% were found to be turning away non Internet Explorer (IE) users and 7% of the sites included non-standard code recognised only by Microsoft's browser.
"Surprisingly, after all these years, users of standard-compliant browsers are still faced with sites that do not support their browser or with a link suggesting they download Internet Explorer," said Deri Jones, chief executive of SciVisum.
This is largely because web developers are used to testing their sites just using IE rather than so-called standards-compliant browsers, which only use code ratified by the World Wide Web consortium.
"There is a certain business logic to this as IE is the most widely used browser," said Mr Jones.
Microsoft is working on a new version of IE, largely in response to the success of Firefox.
"Companies who value their brand need to address browser issues immediately," said Mr Jones.
Web developers who create code around the web standards recommended by the World Wide Web stand to gain more than just friends among the alternative browser community.
It will also make it easier for disabled people to use, said Mr Jones.
"Over time developers have begun to misuse the original standards created for the web to create websites that look great to you and I, but are confusing to a disabled person using a screen reader which needs to make sense of the content," he said.
Simplifying things by separating content from presentation will have a third benefit in that it will make it easier for sites to be picked up by search engines, he added.
Firefox has been created by the Mozilla Foundation which was started by former browser maker Netscape back in 1998.
The group is an open source organisation which means that the creators of the browser are happy for others to play around with the core code for the program.
Firefox is proving popular because, at the moment, it has far fewer security holes than Internet Explorer and has some innovations lacking in Microsoft's program.
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