1 How one became a Dutch Politician
The Dutch politicians of the era were a strange lot. The primary political arena of the United Provinces was the city. Once a politician came into office in a city, he could be sent to represent that city in a provincial 'staten' (assembly or état). The provincial state could then send him to the States General, and in this manner, Dutch civilians could rise to the highest offices. The entry point of such a career was however restricted to the members of those families that traditionally held power in a city. Therefore all Dutch politicians were essentially city magistrates.
The problem that in my opinion eventually led to the downfall of the United Provinces was concentrated in this entry point. The traditional route to office was that someone got rich in trade and then entered a city's magistrate and got into power. This way the members of the most vigorous families entered office and the United Provinces had very good leadership. However, at the turn of the century this mechanism crumbled. Some successful traders still got into office, but most of the officials (regenten) had inherited their office and were often void of any capability to govern. The era that concerns us would see the last generation of great politicians.
Note that in the provinces of Friesland, Groningen and Drenthe the rural population still had a part in government. In Overijssel and Gelderland the nobility was still influential.
2 Dutch Political parties
There were indeed two political parties in the United Provinces. The Orangist party stood by the policies of William III, and thus opted for a strong army, cooperation with England and centralized authority. The 'States' party generally favored provincial authority, attention to the navy and economizing on the army.
Heinsius, Fagel, Hop and Slingelandt can all be considered to belong to the Orangists because they adhered to William III's policies. After his death this had less meaning than before. It did not mean that these politicians were for appointing his still young successor as Stadholder, even though they were perhaps inclined to further his career. Really Orangist politicians therefore have to be sought near the court in Leeuwarden. Really anti-Orange politicians could be found in Zeeland, which had suffered from the rule of one of William's henchmen. Only in Gelderland, Overijssel and Utrecht there was a serious conflict between the Orange party, who leaned on appointments, and the 'States' party which wanted to do away with the 1673 regime.