On the other hand, as young people come into contact with Buddhism, they appear to be starting to think of it as something they need for emotional support.
Literal
Also on-the-one-hand, young-people [topic-は] Buddhism [to-に] touch [in-the-midst-of-中で], Buddhism [object-を] heart [of-の] support [as-に] necessary thing [quotative-と] begin-to-think [ongoing-ている] [apparent-ようだ].
Written commentary-style sentence with several stacked grammar points. また一方で introduces a parallel observation (the 'on the other hand' contrast with something earlier in the text). ~に触れる means 'to come into contact with (a subject, culture, idea),' not physical touching. ~中で = 'in the midst of ~ing,' giving the ongoing-process reading. 心の支え ('pillar of the heart') is the idiomatic compound for emotional/spiritual support. 考え始めている stacks two auxiliaries: ~始める (begin to) and ~ている (progressive). ~ようだ hedges the whole claim as an apparent trend, not a definitive one.