Op Amp with capacitive load - Peak Detector
I just want to know why this configuration seems to be stable with a
capacitive load.

It's a non-linear circuit that attempts to charge a capacitor when the input voltage exceeds the previously highest input voltage and, there is no basic problem here; it can't go unstable (as I suspect your engineer colleague thinks it will) because it's not a linear amplifier AND, the capacitor is only called into-action when a new high-peak of voltage arrives at the input. That occurs rarely and is of no consequence to stability.
There's a big difference between struggling to drive a capacitive load (which all op-amps suffer from to one extent or the other) and trying to remain stable in the presence of a capacitive load in a linear circuit. This rectifier circuit WILL NOT go unstable unless you have chosen an op-amp that cannot be used in linear unity gain situations (there are a few).
You do need a &quot;light&quot; pull-down resistor in parallel with the capacitor by the way.