Can some types of partners cause more anxiety to an anxiety sufferer than others?

Certainly. If you have anxiety (which is fear of an unknown object or situation) a person who embodies the hidden feared situation can make it worse. Also, a non-supportive or critical partner can make almost anyone anxious, fearing that they are not "good enough.'.
Yes. Patients with anxiety disorder need support and understanding. Living with someone who is highly critical, demeaning, and unsupportive could increase the stress level which in turn will worsen the symptoms in one with anxiety disorder.