I can no longer send texts via "Messages" from my Mac to non-Apple phones.

Hi buribe215,

It appears you are unable to use SMS relay, a Continuity feature in Yosemite. The following article provides basic troubleshooting steps you may want to explore:

Get help using Continuity with iOS 8 and OS X Yosemite - Apple Support

If a Continuity feature like Handoff, phone calls, Instant Hotspot, or SMS messages isn't working the way you'd expect, make sure your devices meet the requirements. Then check your settings.

Check System Requirements

Make sure your iPhone, iPad, iPod touch, or Mac meet the system requirements for Continuity, and for the specific features you want to use.

Check your settings

Check the following settings on your iPhone, iPad, or iPod touch:

• Go to Settings > Wi-Fi and turn on Wi-Fi if necessary.
• Make sure your iOS devices are connected to the same Wi-Fi network by going to Settings > Wi-Fi and comparing the name of the network each is on.
• Go to Settings > Bluetooth and turn on Bluetooth if necessary.
• Go to Settings > General > Handoff & Suggested Apps and make sure Handoff is on.
• Go to Settings > Phone. If you see Wi-Fi Calling, turn it off.

Check the following settings on your Mac:

• Go to the Wi-Fi icon at the top of your screen and turn on Wi-Fi if necessary.
• Make sure your Mac and iOS devices are connected to the same Wi-Fi network. Go to Settings > Wi-Fi on your iOS device and compare the name of the network with the Wi-Fi network on your Mac.
• Go to the Bluetooth icon at the top of your screen and turn on Bluetooth if necessary.
• In System Preferences > General, select “Allow Handoff between this Mac and your iCloud devices.” If you don't see this setting, your Mac may not support Handoff.
• Open the FaceTime app, go to FaceTime > Preferences and turn on “iPhone Cellular Calls.”
• Go to System Preferences, and sign out and then sign in again to your iCloud account.

Thank you for contributing to Apple Support Communities.

Take care,

Bobby_D