It can be shipped, but only under the CITES rules.
Rosewood is still available from Brazil, harvested from the leftover stumps of trees cut pre-CITES. It's carefully controlled, limited availability, and comes with CITES documentation. You can find companies selling bookmatched Brazilian rosewood boards with full CITES documentation with a web search.
There's a good chance that Warmoth may not have proof of origin from their old stocks of rosewood purchased pre-CITES (prior to 1975). In this case it's probably impossible to get an export permit to allow the rosewood to travel cross border to any of the 172 nations that have signed on to CITES. It may also be that because of the paperwork and headaches involved, they don't want or need to go there.
This is a huge problem for anyone with an older Martin or other fine instrument made with Brazilian rosewood. The owner simply cannot legally travel cross border with it without first obtaining a CITES export permit from the exporting country, and a CITES import permit from the country it's going to.... and visa-versa on the way back. Obtaining CITES import/export permits is tortuous at best. There is a movement now to somehow ease the rules in the case of older instruments, but where do you draw the line, and how do you verify older vs. newer? How can you prove that a new instrument made with old rosewood is not in fact a new instrument made with new rosewood?
Some countries, like Canada, have specific instances where importation of CITES items (rosewood, or ivory, etc) is permitted WITHOUT an import permit. I did it once. Specifically, you have to be ex-pat, and repatriating back to the Canada with your household items. In this instance, where you've acquired the items as part of your household inventory as a non-resident of Canada and move back to Canada, Canada deems that the import of otherwise restricted items is allowed. This is not the case if you are simply traveling or vacationing. This was the case in 2005. And it may only be Canada that allows this loophole for their ex-pats. And it doesn't meant that it's legal to EXPORT the item without a CITES export permit from the country you're leaving. It's bloody complex, but at least a Canadian can bring grandma's old piano back with them when they move... the one with the ebony and ivory keys.
There are movements now to restrict rosewoods originating from other countries as they are becoming endangered as well. It's a slippery slope and it's going to get more restrictive over time unless there's a lot more replanting.
In case it hasn't been mentioned before, the reason it's called rosewood is because it smells like roses when it's freshly cut.
cheers
Aerocaster