In most cases, no. Here is the reasoning, so you can judge it for yourself rather than take our word for it.
What was copied, precisely
The number and the identity details recorded alongside it — date and place of birth, country of birth, nationality and sex. These were held as text in a database, because border and port authorities require them for crew and passenger lists.
What was not copied is the document itself: no scan, no photo page, no signature, no machine-readable strip. Any passport copy you uploaded to Quarterdeck was stored separately and was not reachable in this incident. The reasoning is set out in Were my passport or licence documents taken?
Why the number on its own is limited
A passport number is not a credential. It is a reference that is checked against the issuing authority's records, and increasingly against the chip in the physical document. Someone holding the number cannot travel on it, cannot renew it, and cannot pass a document check that requires the passport to be presented or photographed.
Where the number does have value to someone is in making an approach look legitimate — quoting it back to you, or to a third party, to appear as though they are us or as though they already hold your file. That is a persuasion risk, not a travel-document risk, and the defence against it is the same as for any other approach: verify independently. See What should I do to protect myself?
When replacing it is worth considering
Replacement becomes worth considering if you see actual misuse — an application, an account or a border query you did not initiate that references your passport. In that situation, contact your passport-issuing authority, and tell us as well so we can look at your case individually.
Some people will decide to replace theirs regardless, for peace of mind. That is a reasonable personal choice. We are not in a position to fund it — see Will you compensate me?
One thing specific to working crew
Your passport number has legitimately been handled by more parties than a passenger's would be — port authorities, agents and charter operators in every country you have worked. That is not a reason to be relaxed about this incident, but it does mean a new number would not remove your details from those records, and replacing the document does not undo the copy that was taken here.
What does reduce what we hold going forward is deletion. See How do I close my account and delete my data?