Check if it looks the same on openstreetmap.org
openstreetmap.org correctly displays the islands and the relative distances between them!
Sounds like a bug in the app then. Though, OSM apps have their choice on how to interpret the underlying data, so it could be based on a deliberate decision. May be worth reporting if you don't mind revealing your town on their github.
Alternate thought just came to mind - is your map data on OrganicMaps up-to-date?
I hope so. I first heard about it (from this very post on HN), downloaded, and installed the app all within the past 1 hour.
And when I zoomed into my city, it downloaded the map information.
In that case it's as up-to-date as OrganicMaps has to offer, which should be within a couple weeks of OSM's main database.
My city is comprised of several islands, and there's relatively large bodies of water between them (over 100 metres), but this map shows those large water bodies as narrow (1 or 2 metre) river-like things.
I understand this might be the problem of the underlying data source, and not the app itself.
(For what it's worth, both Google and Apple maps correctly displays the islands and water bodies).