The result would be a catastrophe (1985)
Nothing I've worked on has been nearly to this scale, but having management understand and ignore warnings is commonplace.Just today, I pointed out that a backend web service system for an important (HR) function was so insecure that simply putting a single quote in an end-user input field would crash it, and that a SQL injection would be trivial.  After a little arguing from them ("You don't know what a SQL injection is") they changed their tune to "Just put a limit on the frontend", and when I told them that could be trivially bypassed, they said "No one will ever think to try that."  When I pressed further, they continued to "It's an internal app, no one would attack it" then to "And do you want me to put locks on all the doors and cabinets around the office too?"So that's a case where there's some reasonable level of understanding and just a refusal to act.I also recall a time (at a different company) when I discovered a public read/write anonymous FTP server setup  externally facing with no firewall rules.  When I pointed out the problem, they said, "that's what our customers are used to, we're not going to change it." and when I pushed, "No one will ever find it anyways."  Literally less than a month later that server was overrun with illicit content.It happens.  Unfortunately, as we've seen with the Volkswagen debacle as well, it happens even when regulation or (in the Challenger case) human life is on the line.