I’ve tried to stay away from homebrew as I’m still new to gm-ing and I could easily break something. I believe you’re talking aberrant dragon marks. They’re definitely hated by the houses, but they sometimes happens when bloodlines from different houses have children. For example, mark of storm mixed with mark of shadow could potentially cause an aberrant mark. These marks are not recognized, the abilities are mixed. Houses fought to keep the marks "pure". There are Romeo and Juliet type stories where this happened.
Forcing a mark is only rumour and speculation and would only be from the darkest of magic. Depending on the views of the kingdom, using a warforged would either be unacceptable tantamount to putting a dragon mark on another race outside of what’s acceptable to the houses. Or for those that believe the warforged should not have been granted freedom, they could see it as the next "upgrade" that gives them an edge in future war.
As for warforged still being produced, the laws officially say that production of all warforged must have been stopped, all creation forges must have been destroyed and all previously created warforged have been granted freedom. There are rumours that creation forges may still exist, but it’s unproven as yet.