May I suggest a re-frame? Because scientifically, magnetism is a fundamental building block of...reality and physics, so you're going to get a bunch of "No that's not possible" and people having to rewrite the entire rulebook of reality. You're also asking us to write an entire history of an earth without this, from the formation of this unreal planet to the entirety of their scientific history. And, if you're keeping the planet's magnetic field there really is no reasoning that makes sense.
The reasons must be social and cultural in nature, not science-based. So maybe a big experiment gone wrong, making it a forbidden technology. It would have to be a high body count because early experiments did kill people...
Magnetism and electricity is interconnected to so, so many other fields that it's nearly impossible to separate out the supposedly "unrelated" ones.
Maybe get hyper specific with this question, filling in as needed. "Without electricity in the time period of X, how would a society get to Y discovery?" Something along those lines...
Some sample reasons why magnets are a no go.
- Considered the purview of an evil god.
- Considered sacred to the main good god so only their priests are allowed to use it.
- Highly publicized dangers of electricity, and a single catastrophic event or series of events have made this illegal.
- Something else is more abundant. There's another source of energy on this planet that's easier to work with. Magnetism and electricity are still there, but there's something else that's replaced them to propel society forward. You could ask a totally different question as to alternatives to electricity.
(Now, if your aim is atmospheric--maybe you like the idea of candle light or something, set me just say that electric lights, staying up later, are the cause of a lot of advancements in myriad ways--socially, economically, scientifically...It's not clear from the question WHY you want to do this, and sometimes the answers here can solve things better if they know your aim.)
If you wanted them to still use candles or lamps, maybe a corporation has purposefully stunted progress for that particular thing. (Certainly there are better alternatives than fossil fuels in cars, it's just not all that common).