It's kind of funny to give an example that could only be tested with an immense amount of expertise (e.g. does the red-shift scaling with distance match) as an example of the problem of being in awe of the specialists.

You literally have to become one to make any meaningful progress. (I'm no expert but I am confident that you're completely wrong about the conclusion from redshift being that space is expanding! It's just that everything is moving outwards as if there's been an explosion: if you follow one mote in a firework, all other motes are (typically) traveling away from it. That's all! The "space expanding" thing is separate. If an object moves away from you with no inflation, you get a redshift. Hence doppler radar guns, for instance.)

Nobody is stopping you from becoming a specialist, if you're motivated (unless your skill level is too low to have the capacity to make a contribution)! Specialists coming up with better models of reality is part of the standard scheme for how scientific knowledge spreads.

It is true that dogma tends to get entrenched everywhere, including in the sciences. The only small hope we have is that in the hard sciences, there's a very clear path to overturning dogma (but it's mostly not "non-specialists coming up with ideas that they think are soooo clever"). Everywhere else it's murky.