htaccess exclude one url from Basic Auth

Using SetEnvIf, you can create a variable when the request starts with some path, then use the Satisfy Any directive to avoid having to login.

# set an environtment variable "noauth" if the request starts with "/callbacks/"
SetEnvIf Request_URI ^/callbacks/ noauth=1

# the auth block
AuthName "Please login."
AuthGroupFile /dev/null
AuthType Basic
AuthUserFile /xxx/.htpasswd

# Here is where we allow/deny
Order Deny,Allow
Satisfy any
Deny from all
Require valid-user
Allow from env=noauth

The allow/deny chunk of directives says that deny access for EVERYONE, except when there is a valid-user (successful BASIC auth login) or if the noauth variable is set.