My nan was breastfed by her aunt because her mum could not feed her (not sure why). At a time when formula was, firstly, expensive, and secondly, of dubious quality, this was probably a good option.
In previous centuries, loads of children were wetnursed.
There is a human milk bank at our local hospital, whereby mothers with an excess of milk can donate bags for consumption by newborns and premature babies whose mums are unable to feed them for whatever reason, and has health benefits for these little ones.
As long as I had given my consent, I wouldn't theoretically have a problem with another woman feeding my baby (if, for example, I became ill). TBH, I'd probably prefer it in the short term to giving formula. That said, I can understand how you might feel side-lined as a mother if someone else was developing that close bond with your baby.
Up to the individual I'd say, but I don't think there is anything remotely yucky or unnatural about it.