why do websites keep saying my browser is out of date when apple states i have the most current version of safari?
Why do websites keep alerting me my browser is out of date when according to Apple i have the most current version of Safari?
Safari's most current version is Safari 9, but poorly written websites often perform a completely pointless "browser check" that might prevent them from loading.
Assuming that is the case you can enable Safari's Develop menu, and choose a different "user agent" that placates the website.
If you are not using OS X 10.11 "El Capitan" then you are using an earlier version of Safari, but no recent version ought to be considered outdated by any website.
Perhaps if you were to post an example of a problematic website's URL someone might be able to offer additional assistance.
