I'd say the best way for you to be judge is to take a look yourself if you can. The previously mentioned episodes 'stickbird' and 'baby race' are excellent examples of how the show appeals to adults as well as children.

It's not overt in trying to appeal to parents with cringey side-jokes or too advanced themes.

It's more situational - for example in baby race, bluey's mum Chilli recounts comparing baby Bluey's progress against the other babies at playgroup - a situation many (all?) parents can relate to. She (SPOILER) gets advice from a friend and learns to 'run her own race' - the concept that Chilli is trying to teach Bluey when she compared to her younger sister Bingo.

The whole show really is a masterpiece. I particularly like the music, and the fact that it's set in my home town 🙂