It has come to the point where Japan is being called a 'measles exporter' by the world — a remark that could be read as either sarcasm or a plain statement of fact.

Literal

World [from-からは] measles-export-country [quotative-と] sarcasm [as-also-とも] honest-opinion [as-also-とも] can-take-[attributive] thing [object-を] is-being-said-[passive-ている] state-of-affairs.

A rueful editorial/op-ed sentence. 始末 at the sentence end gives a 'has come to this dismal state' nuance — 'to such a state that X.' 嫌味とも本音ともとれる 'can be taken as either sarcasm or a plain honest statement' uses the repeated ~とも frame to list alternative interpretations ('either as A or as B'). 麻疹 ('measles') — Japan was criticized in the 2000s–2010s as a measles exporter due to low vaccination rates. The 【】 corner brackets set off the quoted phrase for emphasis.