Inbreeding, per se, likely wouldn't cause the majority of your order to drop dead during or just after the shipping process.  I mean it COULD, but probably would cause the chicks to just not hatch in the first place, or cause evident defects like cross beaks, leg problems ,etc.
More likely is something about the shipping- when the whole order dies like that it's usually because chicks got too hot, too cold or were in transit too long.
I have never ordered from cackle myself because of all the posts on here about their less-than-stellar customer service.  Not just one person, but several have posted about lack of communication and order screw-ups.  That makes me more leery to order from them than hearing your chicks didn't make it through transit...
https://www.backyardchickens.com/forum/viewtopic.php?id=60441
That's the power of a forum like this though - it allows people who may have thought their experience with a particular company or egg seller, etc was unique, only to find when posting that there are several, or even MANY others with the same issues with the same sellers.
I say to everyone....be thoughtful before posting anything negative about any company....  For me, I'd not post anything negative until I'd had a chance to actually follow up or attempt to get satisfaction from the company/seller first.  There's a huge difference in my mind between having a problem and then getting prompt and courteous resolution and attention when I notify the seller, and getting rude responses and bad customer service...