Recognising that a flag is indicative of a military faction is one thing
But all the nations which have dealt with Confederate merchant ships so far have acknowledged that they don't belong to the US either:
'Towards the end of June 1861 a merchant-vessel under the Confederate flag made her appearance in the Port of London. This was the first case of the kind... The Peter Marcy therefore remained unmolested in the Victoria Dock, flying her Confederate flag.
As early as the preceding April the same question had been raised at St. Petersburg by the American Minister (Mr. Appleton). Prince Gortschakoff had answered that, while things continued as they were, commerce between Russia and the Confederate States would not be interrupted... If they chose to deny that they belonged to the United States, that would make no difference. This involved no recognition of nationality; it was a concession in aid of commerce. Regulations to this effect were subsequently issued by the Departments of Marine and Trade...
A similar course was adopted, but not without dispute, by Spain. The Governor of Cuba having issued an order under which "vessels proceeding from and bearing the flag of the Southern Confederacy" were to be permitted to enter and clear "as vessels proceeding from a foreign nation which had no accredited Consul within this territory," Mr. Seward wrote to Mr. Schurz to express dissatisfaction. His Government expected, he said, "that such vessels should be treated in all respects as American, and subject to the laws and consular authority of the United States"... Senor Calderon Collantes refused to comply with this unreasonable requisition...
These cases fairly represent the general course which nations may be expected to pursue in respect of the unarmed ships of a revolted community, whose independence has not been recognized.'
('
A historical account of the neutrality of Great Britain during the American civil war,' Mountague Bernard)
Under the 1842 agreements the RN is obliged to request a US ship to intervene if it wants to stop a US flagged ship. The Confederacy is not US flagged - it doesn't fall under the 1842 convention.
This isn't quite correct. The Webster-Ashburton treaty doesn't say anything about the Royal Navy being 'obliged to request a US ship to intervene'. What it says is:
'ARTICLE VIII. The Parties mutually stipulate that each shall prepare, equip, and maintain in service, on the coast of Africa, a sufficient and adequate squadron, or naval force of vessels, of suitable numbers and descriptions, to carry in all not less than eighty guns, to enforce, separately and respectively, the laws rights and obligations of each of the two countries, for the suppression of the Slave Trade, the said squadrons to be independent of each other, but the two Governments stipulating, nevertheless, to give such orders to the officers commanding their respective forces, as shall enable them most effectually to act in concert and cooperation, upon mutual consultation, as exigencies may arise, for the attainment of the true object of this article; copies of all such orders to be communicated by each Government to the other respectively.'
It's phrased this way because the default position is that you're not entitled to board a foreign-flagged ship unless you have a treaty with the appropriate power which permits you to do so, or you're claiming belligerent rights. The British in 1842 claimed that they had a right to stop a ship and confirm that its flag matched its registration; the Americans disagreed, arguing that it was for the power whose flag was being misused to detect and punish infractions. It was the American interpretation which won out, with the quid pro quo as embodied in this clause being that the US would station more ships on the African coast so the British wouldn't need the right of visitation.
Britain didn't sign conventions with other European countries agreeing to refrain from boarding their ships. It signs conventions permitting it to board their ships, and it does so because of that default position that you have no right to board.
Essentially the RN can treat the Confederacy as a ship of unknown origin and once it is boarded the US citizens may be entitled to US protection (not CSA - yet).
"I didn't recognise the flag" cannot be an allowable excuse for boarding, because absolutely any captain could claim not to have recognised a particular flag. Board whoever you want, and then brush it off afterwards by protesting bad weather or bad eyesight. A naval officer can request that a ship not flying colours displays them, and can fire a gun to coerce them into doing so. If he thinks they're flying false colours and the ship actually belongs to his nation, he can board them. But he better be damn certain if he does, because if he gambles and loses, it's the right of the power whose rights have been infringed to demand and exact reparation.
The British government has recognised the Confederacy as the de facto government of the American South for several years. It has empowered its consular agents to treat directly with Confederate officials where British interests are at stake. It's not feasible to revert from that position to 'this nation doesn't exist', particularly when you've already dealt with their merchant ships as if it does, though it may be feasible to make the legal decision that the Confederacy has inherited the international obligations of its predecessor state.