Unplugging power cords from amps/ pre amps

+1 @onhwy61 I suppose it matters more if you have a substandard power grid and/or live in an area with crazy storms, but I’ve lived in the New York City area and Chicago my entire audiophile life (about 45 years, 40 of which my components were all plugged directly into the wall) and never unplugged my equipment due to storms and have never had an issue.  Maybe I’ve just been lucky or have robust equipment, but all my stuff since five years ago runs through an Audience power conditioner and that’s enough to keep me from yanking power cords every time I hear thunder — just not gonna do that.  If I was really that concerned, and as onhwy61 mentioned, I’d get a whole-house surge protector and continue to live dangerously that way.  Maybe I’m just whistling past the graveyard, but I’m not letting every potential storm stress me out — too many other things to worry about and stress over.  But that’s me.

Does anyone unplug all the electronics in their house...

My stereo is easily the most expensive and hardest to replace, so I naturally unplug it.  I also unplug my computers and welders, but they're just expensive.

Do you own your own home ? 
do you have a dedicated 20 amp. Line 

IHave several layers A Siemens home surge protector handles small as well as big surges at your breaker box.  VH Audio has a great surge protector with power factor correction. You put on your specific breaker.

if you have $$ there are dedicated Battery 🪫 systems you can play music a solid 8 hours or more .

Does the manufacturer specifically warn to unplug the power cord only at the receptacle and not at the equipment? 

Since the power cord detaches at the equipment, it is reasonable to assume that some end users would find it more convenient to plug/unplug at the equipment end. If that is a problem for some reason then a caution would be printed on the owners manual and the back of the equipment. Also, the equipment end is chamfered to fit the receptacle, preventing inadvertent polarity switching. All these signs point to it's okay to unplug everything from the equipment.

@OP There is no problem unplugging your equipment at the component end. Just  be absolutely sure to do it after turning off the relevant components.

The biggest risk in thunderstorms is to anything that's connected to an antenna like a radio aerial or satellite dish.

I have seen fires started by lightning strikes to such equipment.