One among many issues faced by iphone users after upgrading Apple iOS verion to IOS 11, text message issue is also reported where users is unable to send contacts over text message or SMS. The option to send via text is just not showing, it can only be shared by email. Users have tried hard and soft reset but nothing seems to fix this.
How to fix Not able send text messages over contacts in iOS 11
Quite possible that due to firmware (company software) being on your phone - much of the firmware is not compatible with IOS 11. It takes over management of the device, apparently isn't compatible with IOS11.
Removing the app's management restored ability to send my contacts via text message. Commonly used ones are MobileIron or VMware AirWatch and similar. So take a look at your profile settings in Settings > General > Profile and see if your iPhone has a profile installed. If so, and you have permission, tap Remove Management. This should fix the issue but if does not try Instead of "Profile," go to Settings>General>VMware Airwatch and found the Remove Management button.
Here's another way to find out what is managing your device for those still having issues (and if this is your problem): Settings>General>Device Management. You can remove management here if your company's firmware is installed and is managing your entire device and interfering with IOS11 functionality.
Now you need to check what all firmware are in your iphone device eg one user came to find out that the Google Device Policy from his employer was restricting the ability to share contacts. After he removed it forthwith, and now messages is viable option to share contacts.