You have raised a very valid point. There does seem to be a serious semantic problem with the second clause in the following sentence:
“The Philippines is the third largest nation in the world believing in Catholicism, and the only one aside from East Timor that is predominantly Catholic in Asia.”
Indeed, if the Philippines is the “only one,” how could there be an “aside from”?
The preposition “aside from” means “in addition to” or “except for,” so that second clause can also be written as follows:
“the only one in addition to East Timor that is predominantly Catholic in Asia”
or
“the only one except for East Timor that is predominantly Catholic in Asia”
The sense of “the only one” does contradict the sense of “in addition to”; similarly, the sense of “the only one” contradicts the sense of “except for.” We have here two distinct entities of the same class, the Philippines and East Timor as predominantly Catholic countries in Asia, so none of them can be “the only one in addition to the other,” and none of them can be “the only one except for the other.”
So how do we get out of this grammatical and semantic conundrum?
I think we can do so by stating the fact as it is: that there are indeed two predominantly Catholic countries in Asia, namely the Philippine and Asia.
We can neatly do just that by reconstructing that sentence as follows:
“The Philippines is the third largest nation in the world believing in Catholicism; along with East Timor, it is one of the only two predominantly Catholic countries in Asia.”
Now the contradiction of terms is gone and the sense of the sentence has become crystal clear.