Netflix and Amazon won't work in any browser under Sierra.

Heather Hilson Said:

”Okay - I ran Malwarebytes and Avast and all came up clear[...]”

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Rid of Avast - It Gets in The Way.m:

Security Software gets in the way on a Mac, and this is a pure example why. Most likely, you are being disallowed access to/from those sites, by Firewall Settings and the like.

Use an Uninstaller to Remove it:

To remove this use download the Uninstaller from the manufacturer, and none other. Just dragging-and-dropping it into the trash does not rid of all software (cache remains). Restart your Mac, once removed.

MalwareBytes for Mac is fine, should it have been downloaded directly from the developer or the AppStore.

Heather Hilson Said:

”Netflix and Amazon won't work in any browser under Sierra: Within the last 6 months Amazon won't load on my MacBook Pro. Within the last month Netflix won't open - "safari can't connect to the server". Neither websites open in Chrome or Firefox either and I've tried opening it in another user account and same issue.[...]”

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Reset your SMC and your NVRAM:

Sometimes changes are made to the system and then settings (i.e. for Internet Access) become manipulated, in the technically. So, reset both on your Mac.

• How to reset the System Management Controller (SMC) on your Mac - Apple Support
• How to Reset NVRAM or PRAM on your Mac - Apple Support

In Safari, Clear Your Temporary Internet Files (History and Cache).

Or...

As a Last Resort, Reinstall your macOS, Create a Time Machince backup, prior to doing so. That way, you’ll have something to restore your Mac from, should anything go wrong.

If you really tried all of the above, something is wrong with your internet connection device's firewall ports. Modems and routers that are open like the WiFi network named XFinity may limit access to secure sites like Netflix and Amazon. You need a secure WPA2 WiFi, or hard wired ethernet connection to your own modem from the internet provider to be able to manage secure connections.

If you are on a secure connection, you may have Malware on your Mac. Run Malwarebytes and Avast to check to see if you have any infections. Also if using Chrome, check to make sure its policy page is not infected. chrome://policy

Lastly, run hhttp://www.etrecheck.com

and copy/paste its results here. That may inform us of other potential malware blocking your ability to use secure sites.