I believe that Sharjah, with the rest of the Emirates, was still a British protectorate at the time that this was minted. That the British were able to enforce the use of the Indian Rupee and then (for a few years) the Gulf Rupee in the Emirates would seem to indicate that they retained control over currency in the region (no idea if this was de jure or just de facto control).
The British were also able to remove the Sheikh from power in 1965 (the same year that these were issued) and he led a failed coup to regain power after independence. Those factors probably didn't help with creating any sense of legitimacy for these pieces either inside or outside of Sharjah.
