If it's asking for a password, it sounds like it's probably coming from IE's Content Advisor (parental filtering) or perhaps from an antivirus program, many of which also have parental filtering capabilities. If that's the case, it's due to the configuration, not the browser version.
Parental filtering usually allows blocking by category. Not all the categories are dangerous or unsafe. Some of the categories exist just so parents can determine what kind of content their kids are allowed to see.
You'll need to determine the reason your site is being blocked. Look through IE's Content Advisor (Internet Options > Content > Content Advisor), and see if your site might fit into any of the categories that parents are allowed to block. Even if it doesn't, it looks like there is also an option to block sites that don't fall into any known category, and parents can also use a "whitelist" approach, meaning that ALL sites are blocked unless the parent has specifically allowed them on the exception list.
If you use an antivirus program, look through its parental filtering features, too, to get an idea how those work. They probably all work pretty much the same, except that different companies have different category lists, and most are probably better and more flexible than the IE Content Advisor.
You might look at the possibility of labeling your site with ICRA content labeling.
But before trying to fix the problem, you'll need to determine more specifically what the problem is. Where is that warning coming from? What password is being requested?
Just as an example, one category some AV programs allow parents to block is "Games". If your site is games, there's nothing you can do about this. Some parents just don't want their kids playing online games.
On the other hand, if an AV program or some other content rating service has categorized your site as Games, and it isn't games, then you can try to get the site properly moved into its correct category.