Should I be around cats if I have copd?

Depends... If you are allergic to cats you should avoid them since this can lead to bronchospasm and airway inflammation, causing a worsening of your symptoms. If you don't know whether you have a cat allergy, see your doctor since testing can be done and then advice can be more accurately given!
Yes. COPD does not mean allergy to cats. If you find that being near cats you get more difficulty breathing or wheezing, sneezing, cough then you may be allergic to the cats besides having COPD or the diagnosis of COPD is wrong.