You certainly see these claims made often. Someone with an anti foot orthotic agenda will say “Do not use foot orthotics as they will weaken the arch muscles“. Those with an anti-running shoe agenda will say something like “Running shoes will weaken the muscles which is why you should run barefoot.” Given the strength that these assertions are made with, you would expect there was some good evidence backing them up. Well, there is no evidence that foot orthotic or running shoes weaken the muscles.
There was this commentarty on running shoes: Do running shoes weaken muscles? and this commentary on foot orthotics: Do foot orthotics weaken the arch muscles?
From what I can understand is that running shoes do not weaken the msucles and foot orthotic do not either – they may even increase it!