Danish dockworkers join Swedish strike action against Tesla

Yes it is legal. It's always legal to strike in Denmark.

It might be a breach of the collective agreement, but it's never illegal by law.

Normally, a strike is in breach of the collective agreement when it happens in a period in which an agreement has been made. They're only allowed to start a strike during the negotiations in between agreements.

A sympathy strike is different though. It's not a strike against the employer. The collective agreement is still in force. What they're doing now is that the employees union warns the employer union that they're going to do this. The employer union can then allow it or not. However the main agreement also contains a list of companies and unions that the employee union are allowed to sympathise with without breaching their own agreement, so if the Swedish companies that are striking are on that list, then the Danish employer union has to allow it. Otherwise it would be the employer union breaching not just the collective agreement but also the main agreement which is the "founding law" of all collective agreements.

So on a very technical level, it might actually be illegal by law for the employer union in Denmark to stop the employee union from sympathising with the Swedish union.

Tesla will also be out of luck trying to challenge this legally. Since they're not part of a union, they don't have access to the employment court that deals with these laws. They can only attempt a "civil case" in the regular courts who don't have any jurisdiction over this. They'd loose by default and it could take several years to escalate it to a higher court which would likely also dismiss it. They'd need to be very creative to make a case that crosses the different branches of law. It's like challenging the constitution. No court would put up with that for one single company that doesn't play by the rules.

Within Danish law, yes. This is a so-called 'sympathy conflict' which is legal. The Danish model for the work market is that conflicts are legal until a signed agreement exists with a union.

When a signed agreement (overenskomst) exists, strikes are not legal until it is time to renegotiate the agreement, which happens every 4 years.

This system was put in place in 1899 following a four month lockout of more than half the Danish unionized workforce. In the end, the workers won the right to unionize, and the employers won the right to lead and distribute work under the terms on the specific agreement made with the unions.

As a result, Denmark does not have state mandated minimum wages or really much state meddling in the work market. It's all self organising to a degree.

Edit: Here's a bit in English about the September Compromise in 1899

They are refusing to sign a collective bargaining agreement with the unions representing their Swedish workers.