It's understandable that some people get anxious at the thought of walking into a hospital.

Literal

Hospital [to-に] stepping-in thing [object-を] thinking [when-と] anxious becomes person [subject-が] existing [topic-のも] no-wonder [copula-は-ない].

無理はない means 'it's no wonder, it's understandable.' 歩み入ること ('walking in') is a formal verb. The whole sentence validates people's hospital anxiety — a culturally sensitive observation.