I presume they are an integral part of some analogue loop; are they the rather expensive "milspec" range? If so, not replacing them unless proven faulty seems prudent.
In that particular instrument, HP used them for almost every application that called for capacitance between 0.47 and 100 uF. Among other places, they were used for point-of-load bypassing, LF coupling, emitter degeneration, noise suppression, and general-purpose feedback/control loops. PLL loop filters were more likely to use film capacitors that don't cause much trouble.
The axial electrolytics weren't inherently bad parts like the SMT electrolytics that you see in Tektronix gear, so they don't need to be replaced unless actually defective. It's very obvious when they are. The bad caps will either appear open on the ESR meter, or their ESR will be several times higher than other capacitors on the same board with similar ratings.
In fact, the bad caps often show some visible corrosion. Those should obviously be replaced regardless of what the meter says.
Is the ESR specified somewhere? If not, what can you presume from a measured value of X ohms?
There's often a chart on the meter itself that shows what ESR to expect for a good capacitor with given voltage and capacitance ratings. Usually less than a couple of ohms. Most capacitors will pass that criterion easily, even after 30+ years. Opinions vary, but I like to replace anything that's over 2x the value in the chart, or that's more than 2x worse than identical parts elsewhere on the same board.