Escaping the declining birthrate requires an increase in unmarried mothers, yet Japanese public opinion for some reason avoids this debate.
Literal
Declining-birthrate [from-からの] escape [for-には], unmarried mothers [attributive-の] increase [subject-が] essential is-[although-のに], Japan [attributive-の] public-opinion [topic-は] somehow this debate [object-を] is-avoiding-[continuous-ている].
Editorial/op-ed register. 少子化 ('declining birthrate / shrinking child population') is one of the most-discussed social issues in modern Japan. 脱却 ('escape, breaking away from') is a formal noun. ~からの is the composite particle 'from X + attributive' — '[something] from X.' 非婚 ('unmarried, non-married') specifically means 'unmarried by choice' rather than 未婚 ('still unmarried'). のに ('although, yet') marks the contrast between necessity and avoidance.