Why do you think many Stalwarts argued that ending the spoils system was contrary to the democratic heritage of the US?
The spoils system was introduced to the US (or was at least made famous) during the time of Pres. Andrew Jackson, who was the hero of the Democratic Party for a long time. The Stalwarts would have agreed with Jackson that the spoils system was more democratic than a more merit based system such as was set up by the Pendleton Act.
A civil service system puts people in bureaucratic office based on their knowledge and expertise. This is, one can argue, undemocratic because these people are not elected nor are they appointed on the basis of political affiliation. You can argue (as the Stalwarts would have) that when Democrats are elected to office, the people want a Democratic government. That means Democrats should be appointed to the bureaucratic positions.
To this way of thinking, it is more democratic to have elected leaders appoint whoever they want to all the bureaucratic positions instead of having those appointments made simply on merit and with no regard to what the voters want.