LiPo charging in consumer electronics (less than 1C?)
It of course varies from chemistry to chemistry.

But also from manufacturing procedure to the next.

A good manufacturer of batteries knows what they are doing and can give you very detailed specifications for allowable maximum rating, advised rating and absolute peak rating. For LiPo there are many cheap manufacturers that get relabelled and resold and then, well, you can't be sure and you might be best off to stick to 0.5C, because a cheap manufacturing process in the Lithium trade can create unequal surfaces and high currents may then cause very annoying aberrations on the "plates" of the cell. Which is bad for its life span to the order of NO!

If it's a very doubtful cell I'd say don't even go over 0.25C.

But with increased experience and insights in how to make a good Lithium based cell, there are procedures that create cells that handle 5C charging with only a 10% decrease in usable life cycle, which in many products can be very desirable.

So, to TL;DR:
If you know the battery's specification, because it comes from a reliable source and with a datasheet showing many charge and discharge graphs and such, you can go by whatever it says. If it doesn't, at least stick to below 1C, if possible to below 0.5C.

(Very good factories even include a graph that shows Charge and Discharge current effect on expected average cell life time in cycles)