I'm going assume that by "smoking" you are meaning tobacco and will answer your question as such although its much the same as what it would be for cannabis:
I am currently taking 50 mg Enbrel injections and I have been a pack a day smoker for over 5 years. I, so far, have not experienced much difficulty or interaction between the two personally.
However, because Enbrel is such a strong immunosuppressent, inhaling any type of smoke regularily (but especially tobacco) will cause damage to your lungs and lower your natural bodies immunity even further.
The main risk of smoking on Enbrel is an increased rate of respitory infections leading to chronic bronchitis, pneumonia, and emphazima. Personally I have experienced minor breathing problems, and a persistant cough due to my smoking but as far as I can tell it has caused no other further problems.
However, if you do smoke while on Enbrel and do get one of the more serious infections as previously mentioned being a smoker will inhibit your body from fighting off the infection (that smoking caused) and will lower your chances of successfully recovering from said infection.
PLEASE NOTE THAT SUCH SERIOUS INFECTIONS CAN AND HAVE BEEN REPORTED TO BE FATAL IN PATIENT WHO ARE TAKING ENBREL. SMOKING WILL ONLY INCREASE YOUR RISK OF AN INFECTION RESULTING IN DEATH!
All in all your best bet is to cut back as much as possible while on enbrel and at the first sign of a potential resperatory infection, call your doctor right away!
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