Kinda depends imo. Would it be helpful to be able to use them as a reference/let them be called when applying to future jobs? You most likely want to give them the notice, especially if the current place is a stepping stone in your career or you have been at the current job for a while. Have you been there 2 months getting the brunt of abuse and not getting anything other than a paycheck? Call it a wash and leave it off the resume, fuck them.

As much as I wish we could treat companies as poorly as they treat us, the reality is that we all have lives to live and it can fuck our personal lives to live our values 100% of the time, as much as it sucks to navigate our system. That's why unions are strong, we have strength in numbers. When we're acting individually though, they hold the power.

So if you need to job hop realistically it's probably better for your prospects to play it safe and do the "proper" thing. Making a stance by setting your future prospects on fire is a dangerous move to you personally that probably won't further the cause toward an equitable workplace. Being able to leave a bad work environment for a better one (possibly unionized even), is the better choice, and if playing the employer's game is the best way to get to greener pastures then I would give notice and all that junk.

Even if you have the next job lined up, you still have to think about how it will look to the new employer if they know your current job and see that you aren't giving notice. They might not take that well and recind the offer (which may be illegal depending, but when has that stopped a company from doing something). It's a stupid game that we shouldn't have to play, but I think you should always weigh your options so you don't mess up your own livelihood. No sense in being a martyr if it won't help the cause.

If you had the chance to know him ... which would your grandfather had done ? I have found that concordance with some cultural norms are best analyzed by reverse leapfrog back over your pop's generation and asking gramps again.