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Also I'm pro-union and not averse to laying out links between fascism and corporate capitalism, but I think you'd need to add a bit more argument here beyond 'the Nazis also did this so it's definitely bad'.
It's fair to say that union busting was a specific part of the brown-shirt agenda but beyond that it's probably not a very useful historical analogy. There was a much more direct link between worker organisations and nascent revolutionary socialism. IMHO Nazi antipathy to unions was more about political competition than preventing increased worker's rights.
It would be more analagous if it was a republican allied political group working to disrupt unions because they were organising to support democrats.