It's okay to be proud of callouses and dirt under your fingernails if you like, but there's nothing wrong with properly trimming your nails and cleaning under them as well, and certainly nothing wrong with lotion on your hands to keep them from getting dried and cracked.
My workplace manufactures food products, and we are not permitted to have fingernails that can be seen from the palm side of your hand, nor are you permitted to have fingernail polish, fake fingernails, tips, etc. etc. I have to keep my hands clean as a requirement of work, so I either use disposable gloves when doing my mechanic work, or reconcile myself to an arduous scrubbing with Lava, Gojo, or whatever. Yes, I have a farm and get my hands dirty quite often, but so far, they've come clean everytime.
You can wear dirt under your fingernails as a badge of honor if you wish, but to me it demonstrates either a lack of hygiene or lack of caring. I would imagine some folks like to have the dirt under their fingernails so that they can show other people how hard they work, but my ego doesn't need for other people to know that - all they need to know is that my hands are clean.
To each, their own - that's what's great. And FWIW, I'll still shake hands, dirty fingernails or not...but I'll wash 'em before put them on my bride...
Good luck and take care.