I am getting the same issue with Pro1x on 4.4.0.64, and unfortunately Waydroid seems to depend on dnsmasq so while uninstalling it fixes the browser, it comes with a significant cost:
[root@Pro1-X defaultuser]# pkcon remove dnsmasq
Resolving
Querying
Testing changes
Finished [ ] (0%)
The following packages have to be removed:
dnsmasq-2.86-1.4.2.jolla.aarch64 A lightweight DHCP/caching DNS server
waydroid-1.2.0+git6-1.6.2.jolla.noarch Container-based approach to boot a full Android system
waydroid-gbinder-config-hybris-1.2.0+git6-1.6.2.jolla.noarch gbinder config for hybris ports
waydroid-runner-0.3.1-1.4.2.jolla.aarch64 Waydroid session wrapper
I’ll try disabling sandboxing as @Seven.of.nine advised above, instead.
[Edit]
Sadly adding Sandboxing=Disabled to the [X-Sailjail] section just breaks the launcher shortcut for me, pressing it no longer starts the browser.