Dummy it up!
I would not "blur" anything. Blurring doesn't allow anyone to view the typeface you chose or it's actual size very well.
Just replace any actual personal information with made up names and numbers.
There's no need to share the information of others in a portfolio. This is especially true if the items will be viewed online.
I've done business cards for Disney characters, South Park characters, my favorite band and its members, movie casts, all using fake numbers and email addresses. Generally, since there's a logo, it's okay to use the actual URL for the company (it's advertising) if a URL appears on the card. For email addresses, I change them all to the same address like
firstname.lastname@example.org. Phone numbers typically use the 555 exchange like in films, since it's a non-working exchange, then just 1234 or some random combination.
Interesting note, is that this can also be used to share a bit more about you and your likes... if the person viewing the items is also familiar with the names, that can spark a conversation.
The actual contact information for a person is irrelevant when looking at business card designs. What is paramount is the type choices, size, placement, etc. That can all suffer if you "blur" the type.