Such discussions often focus entirely on the rights and responsibilities of pubic servants as citizens. But they also need to encompass the rights and responsibilities of elected officials, as employers. It is their responsibility too, to maintain the institution of public service as non-partisan in nature.
The really tricky bits occur when the agency employee themselves becomes an unwilling campaign tool for the politician. Public servants have an obligation to carry out the lawful policies and activities of the government of the day, but they have no obligation, legal or otherwise, to be a shill for that government and help them be re-elected. As at least one major report I’ve read indicates (based on a survey of hundreds of public administration grads now in public sector positions at various levels), over-enthusiastic political staffers sometimes have a difficult time knowing where the line is drawn in terms of co-opting public servants for partisan activities.
The political impartiality of the public service is an important value to support in a modern democracy. I think it’s everybody’s business to work/act in support of that, whether you’re elected or not. Which is probably why political expression within the workplace is probably less than a best practice, no matter what the level. It runs the risk of making co-opted political support look too normal. But that’s MY paranoia; doesn’t have to be yours.