It wouldn't stop me from joining a company that's clearly better than the rest. But engineers have a lot of comparably good options in hub cities, so it's reasonable to be picky about small stuff - we can afford to be. A formal dress code does have real downsides: it (1) costs money, (2) wastes closet space (it's a premium in NYC!), and (3) makes biking to work or otherwise living a pre-/post-work active life more of a pain.

Most other things being equal, and they usually are, I'm going to take the job with the more relaxed dress code.

A dress code is a red flag.

It is not about being forced to wear clothes. It is about working with a management team who is so incompetent that they would do something so stupid as implement a dress code.