Is Oral Thrush Contagious?

It is caused by a fungus.  Usually in adults, the immune system is weakened.
 
I wouldn't worry so much about sharing with the family, but would be careful not to kiss them (on the lips) share cups, utensils, etc. With them until it is cleared.
 
 

Oral thrush is caused by an infection of the yeast fungus into the mouth. Adults with weakened immune systems get it and it is highly contagious to other people with weak immune system [like people with HIV]. But the good news is that it is easily cured but until then sharing of eating utensils and any sort or oral contact should be avoided.