I know that there were a few republican groups in England at the time of the french revolution, but i don't know just how big they were, and as was demonstrated by their treatment of Thomas Paine they would crackdown hard on anything they saw as rable rousing very quickly. Plus it helped that the government had a few republican aspects, unlike the ancien regieme
The only real Republican Groups, post-Cromwell, was the so-called "Good Old Cause", however beyond that most anti-Republicanism was more the Gentry's fear about Cromwellianism returning. This is because even as a movement Cromwell's rise to power wasnt really off any popular mandate, but off the backs of his very loyal soldiers, so the peasantry never really had any sort of love for him.
A Stuart Victory in the Civil War preceded by a reign of mass terror by Puritains and Levelers that spooks the elite away from the notion of popular possession of political power (thus retarding later reforms by dragging out the bloody shirt) could lead to the continued restriction of the franchise, a weaker parlament, the dismissal of the merchant class from political power (by tying it to land ownership) in such a way as to slow economic development ect. that could lead to the kinds of conditions that created Republican sentiment and state instability in the early 19th century
Firstly, I doubt the Puritans would perform a reign of terror, as the Puritans were primarily Gentry, and Merchants, the majority of the Rural Population remained Pseudo-Catholic, and even Pseudo-Pagan, for a long time after the civil war. Secondly, the Levellers never had the population to perform a reign of terror, the thing that spooked the Gentry/Merchants about them was that they existed, and doubly so for the Diggers, in fact a key part of Cromwell's Consolidation of power was his crushing of the Army Agitators. Similarly, a Stuart Victory arguably would prevent the rise of so-called Classical Liberalism, and would lead to English Liberalism, and thus American Liberalism, being about comparable to France, from the start. A further complication is that with a Stuart Victory the Northern US Colonies would likely become more Puritan, from refugees, this would likely form a divide between the North and South, that coupled with the Settlements in Canada, would prevent any type of American Independence. The Other issue is that at this time the key reason for the Strife, was the Parliamentary Control of Taxes, which if he had won Charles would have likely gotten greater control of, this along with Loans would then allow for Continental Wars, and colonial wars, likely more with the Dutch, and it is hard to predict, if these would have the same outcome as under Cromwell, and Charles II.
