I'm not sure if this is explicitly documented anywhere, I couldn't find anything, but found references in the source code and in a few PRs.
In order to allow cookies (and other auth mechanisms?) to be passed to a microcks-hosted REST API in a cross domain scenario, you need to set the CORS_REST_ALLOW_CREDENTIALS to true

1. In a docker-compose file:

version: "3.8"

services:
  microcks:
    image: quay.io/microcks/microcks-uber:latest-native
    ports:
      - "8080:8080"
    environment:
+      - CORS_REST_ALLOW_CREDENTIALS=true

2. As a one-liner docker CLI command

docker run -p 8080:8080 \
+  -e CORS_REST_ALLOW_CREDENTIALS=true \
  quay.io/microcks/microcks-uber:latest-native