First try and see it their way. Understand from the business perspective why these decisions are being made. (You might have to dig and ask a lot of hard questions.)
Hard questions uncover hidden truths. Not everyone is comfortable with this, especially if you are changing the status quo. You may open yourself up to attack in an unhealthy culture. Do not do this alone.
Identify places where testing would have saved time (money). Catalog these scenarios as they play out so you can present them later.
Find allies within your company and share what you are learning. Do they experience the same pain points as you? How can you work together to educate and change the culture?
When your group is ready, present your case to the nessesary stake holders. With consensus from allies, draw reasonable lines in the sand together.
Define your process and your definition of done to include the quality measures that add real value to the business.
Measure. Define. Align. Push back together.
Once you've gain acceptance at scale, implement controls to stop quality from slipping in the form of tools and process. Enforce your process with tools whenever possible. Coverage and reviews, realtime quality measures, etc.
If it wasn't worth it, it wouldn't be so difficult.
Go get it.
We're a place where coders share, stay up-to-date and grow their careers.
We strive for transparency and don't collect excess data.