In ArcGIS Online, when using the Share option to share a web map with a group, a Bitly or short URL is generated replacing the organization domain. For example, org.maps.arcgis.com is replaced with arcgis.com. This causes the web map to prompt users to log in when using the short URL if the web map is shared with a group.
When sending a URL to an item or item page, be sure the item is shared in a way that the receiving person can access it. For example, if the item is only shared to an organization, then only members of the organization can access it and its item page, thus they are prompted to log in either using org url or www.arcgis.com (test in a different browser tab of Google Chrome when logged in already is not valid). Share the item publicly If the item has to be accessed without being prompted for login.