I recently bought an Azor Opa style bike with 28x 1 1/2" (700 x 38c) tires that I want to switch out with something slimmer. Would going down to 30c present a problem for my wheel perhaps?
It will depend on the rim width, according to Schwalbe's table of tire size to rim widths you'd be fine with a 17 or 19 mm rim and you'd be pushing it if you have a 21 mm rim.
The bike would sit about 4 mm lower is the main thing (and technically, the gearing will change slightly).
You can mount the tire on there and it will work, but it may not be optimal depending on your rim width; if the rim is too wide for the tire, you may get more flats or rim damage when you hit a road hazard.