There is no way to share the contact info with iOS. It is not hard to do the process, but it is having more than a tap like shareable features that are found in your iDevices. If you want to share information, but if you are interested not sharing enough information including sensitive information on the default card, then you can set up a secondary contact card. But make sure that you have set the default contact card.
Navigate to your Settings > open Contacts > and then Tap “My Info.” It will take you to the contact page where you can easily select the name for setting it as the default contact card. Then you can go to Contacts and edit all the personal information like address, nickname of Siri and birthday and other information.
You can create a secondary card for sharing information to others if you will tap + icon in the upper right hand corner of your Contacts app. You can only fill the information for which you are comfortable while choosing the information to share with others.
For sharing the contact card, open the contact app, then select the secondary name, after that scroll down and tap on share contact. Then you will select how you will like to share the information. You can give an authorization to others by tapping to more option.
This is the way in which how you can share the contact information to other people by using messages app. Suppose if someone is going to ask for the phone number or address, you can easily share the contact card instead of typing it manually.