On other forums, I asked about the clause in question. Someone cited the following definition from the OED:
Sympathy: 3. a. Conformity of feelings, inclinations, or temperament, which makes persons agreeable to each other; community of feeling; harmony of disposition.
His understanding is this:
“[From her and by her example] we held those common sentiments that we shared amongst ourselves and which bound us together.”
It appears that this use of "sympathy" is different from the one most familiar in current English, i.e., feelings of pity and sorrow for someone else's misfortune. If sense 3. a. is assumed for "her sympathy was ours," the rest of the passage (reproduced as follows) would be understood coherently as supporting details:
I might have become sullen in my study, rough through the ardour of my nature, but that she was there to subdue me to a semblance of her own gentleness. And Clerval—could aught ill entrench on the noble spirit of Clerval?—yet he might not have been so perfectly humane, so thoughtful in his generosity—so full of kindness and tenderness amidst his passion for adventurous exploit, had she not unfolded to him the real loveliness of beneficence, and made the doing good the end and aim of his soaring ambition.
With the OED definition, however, the phrasing of "her sympathy was ours" remains peculiar. Perhaps "X's sympathy is Y's" is used by Shelley as a poetic way of stressing (virtual) oneness of disposition.