Is it illegal for jobs to overlap?

I work at an Eikaiwa and my last day is March 31st. The job I got starts April 5th but I have to go for a special work day on March 26th. I asked my boss about it and she said it's illegal for me to work at two full time companies at one time.

Is this true? Even one day? Should I be worried about it?

Probably not illegal, but may be a breach of your contract.

You asked your current boss? Why didn't you just take a regular day off to go do your training?

it is not expected that you have two full-time jobs simultaneously.
if you make some damage to others or properties in the work, the company has responsibility to compensate it. if the company knows you are overworking (because of the two jobs), they can't say any excuse about what you did. the company can expect objectively that you have a higher possibility to make a mistake (or a damage).
if you are a responsible person, you should not have two jobs simultaneously.

It's not illegal, but your boss certainly isn't required to give you a day off to go to work at a new job, even just for training (if you have leftover paid holiday you can use that). It would be a technical breach of contract if your contract says you aren't allowed to work anywhere else while contracted to job 1.

The Constitution of Japan, the Civil Code, and the Labor Standards Act, all grant you the right to work for whomever you want (within the bounds of your residence status).

It's not illegal to have two full-time jobs, nor are you under any obligation to inform one employer about the other employer (or vice-versa).

Non-compete clauses in contracts are null and void due to their illegality.

A recent article on the General Union's website explains things very well: http://generalunion.org/Joomla/index.php/laws-and-rights/1376-illegal-...

Obviously, you still have a duty to ensure that your jobs don't conflict with each other, but that is a personal responsibility.

those unions are generally extreme left. you can't generalize their opinions.

It's not an "opinion". It's the law.