As a convert to Shin/Jodo Shinshu, I believe in Amida Buddha's reality - i.e., I believe that "He" is a real Buddha. Not a Buddha in a "meat body" any longer, but a Buddha operating from the transcendent realm of the Pure Land. This may have a parallel to the Christian belief in the risen exalted Jesus, who no longer lives on earth in an "incarnational body", but rather reigns as a transcendent "Power" in a transcendent Heaven. And most Christians, of course, insist on Jesus' reality. Similarly, I believe in Amida's real, transcendental Buddhahood, even though it has been eons ago and perhaps dimensions far away since he was "in the body" as the Monk Dharmakara.
That is of course not to say that Amida "looks like" any earthly representation of a Buddha or Enlightened person. The Transcendent is difficult for samsaric beings to picture, and inevitably word-pictures fail. For me, this only signals samsara's deficits, not some flaw or lack of reality in the Transcendent. Certain old quips apply here, such as, "How can a butterfly describe its experience in the wide world to a caterpillar", or, "How can a fish - caught and then released - explain to other fish what the air-world is like?"
Amida and the Pure Land may be difficult to picture and conceptualize, but fortunately, the Buddha is known immediately via our reception of Shinjin, in which His providential grace quickens us and grants us a sure knowledge that we are "embraced, never to be let go". For me, this salvific process conveys the Buddha's compassionate essence - and hence, His reality - and since experience trumps belief-in and belief-about, this experience sufficiently bypasses any doubts that Amida Buddha might not be a real Buddha.