I finally retired my knackered iPhone 6 for an iPhone 8, and now it seems the Specialized gloves I was using don't work with the new Home button. Any suggestions for full-finger road/cross type gloves (I don't need a ton of padding) that work well with the "newer" iPhones?

No full finger gloves will work with the fingerprint sensor if that's what you mean. That's a problem in the alpine skiing world - some solve it by using the tip of their nose programmed as a "finger."

Android user. I've always worn thin Merino glove liners. I've been able to use my phone with them. Not the ones with the special fingertip, any thin glove liner has worked for me.

Yeah--I understand that. My gloves have the little texture for using touchscreens--that has always worked once the phone was on. On my iPhone 6, I could push the home button and then type in my password. On this iPhone 8, I can't click the the home button!
Never thought of the nose thing--now that I gotta try!

Brilliant - let's start an argument whether this is a bodge or a hack? I say bodge - the grease from your nose will pfaff the sensor and screen.

OP, I've had a few gloves that allowed me to work my old iPhone 6 plus screen but they always wear out after a few months. I upgraded to an iPhone X last Christmas to get around this - primarily for skiing

Well, the good news is, I live in SoCal. So, I could easily just cut off the tip of the thumb of my worn-out but still serviceable gloves, and never have to worry about frostbite

I have an iphone 8 and the Pearl Izumi Escape Thermal gloves work (full finger, no padding). Had no luck with some full finger (but not cold weather) Giro gloves--couldn't press the home button or anything else despite the "smart touch" fingertip.

I have an iPhone 8 and use full fingered gloves in the cold. It will work, you just need to press the home button it a few times until you get the passcode screen.