How do you handle your Chief saying "This is how we have always done it" when you clearly know its against regs?

As a Chief and an Officer I can tell you that you need to help fix the problem, especially if it is safety related. Take the Chief off to the side (meet with him in your stateroom or the Chief's mess) discuss the issue and have all your ducks in a row. Tell him your true concerns, if you are just looking to follow some stupid rule the Chief will see right through you. If you have a good Chief then they will support your decision and you will gain their respect. If not then look to other senior enlisted leadership for help like the CMC. In my experience Chiefs run the Navy, Junior Officers are their to uphold standards, gain leadership skills, and learn tactics. This is your opportunity to learn some leadership skills.

Just so you know I am dedicated to what I say, I still think 16 September 1992 was the best day of my life. This is proudly displayed in my office today.

Quite simple. "It does not make it right". Honestly, when dealing with your Chief, be direct, succinct and to the point. If they are worth their salt, they will appreciate it. Yes, some steps can be adjusted, however if it is safety related, there is no compromise.