Thank you for such a nice post. There are many schools of Buddhism, and, as I am sure you know in Christianity, faith in Jesus of means different things to different people. Likewise, the different schools of Buddhism emphasize different things.
You asked, "Are these supplications interpreted in a non-literal sense, in which "I take refuge in the Buddha" really means "I take refuge in your teaching"? and the short answer is yes -and no. The Buddha was a person who lived about 2500 years ago. "Buddha" means someone who has awakened to the truth of how things are. When Buddhists "take refuge in the Buddha, the Dharma and the Sangha" it means that the buddha is the example. What he awakened to, you or I can also awaken to. The Dharma is the path to that awakening, and the Sangha is the family of all others who are on this path.
Strictly speaking, there is no god in Buddhsim, the way you would think of god in the Christian sense, as a divine creator, and the Buddha is not the same as a god. So, taking refuge in the Buddha is not the same thing as 'accepting Christ as my personal savior'.
At the same time, you have mentioned some similarities in terms of a 'compassionate spirit'. Buddhism does not maintain any idea of a soul or permanent spirit, but it is generally held that all beings want to be free from suffering, to have peace of mind, to feel loved and so forth. Even tiny insects struggle to live, to not get eaten and so forth. Of course, there are a lot of differences between Christianity and Buddhism, and there is no shortage of experts here who can point out all the technical reasons why the two belief systems are not the same.
I think what you realize is that it doesn't really matter a whole lot what kind of label you put on something. What matters is what you actually do. Christ's "dharma" was the path of forgiveness, and he based that on the idea that we are all not perfect. "Let him without sin cast the first stone" and so forth. "Sin" is not really a factor in Buddhism either. There are things to do and things not to do, but these are there to help one stay focused and end suffering. Forgiveness is not really emphasized specifically in Buddhism, but as I understand it, Christ based his path of forgiveness on the premise that all people are equal (as he would say, "in the eyes of God" --Buddhists wouldn't add that) and in general, this idea of equanimity is shared in the various Buddhist teachings, but based on different sets of premises.
That "'same spiritual reality" you mentioned is compassion-- true compassion, which is unlimited.
It isn't one shape or color, it extends effortlessly to all beings.
I am interested to know what type of Buddhist thing it was that you visited.
Profile Picture: "The Foaming Monk"
The Chinese characters are Fo (buddha) and Ming (bright). The image is of a student of Buddhism, who, imagining himself to be a monk, and not understanding the true meaning of the words takes the sound of the words literally. Likewise, People on web forums sometime seem to be foaming at the mouth. Original painting by P.Volker /used by permission.