I feel like this must be fading because I lived in North Yorkshire for almost 5 years and never heard a thee/thou used. On the other hand, English dialects are hyper localized so there might be villages where it is normal.
I definitely heard it more from my Grandfather, but I still hear it here in South Yorkshire. It seems to be most often used in common phrases, such as "What's tha want for tha tea?" or "What's tha doing?" (tha = thou/thy), or used for emphasis ("I'll tell thee what"), rather than as a general alternative though.
> English dialects are hyper localized
On a vaguely related note, has anyone else (particularly in Yorkshire) use "seef"/"seefing" to mean "see if"/"seeing if" (as in "I was seefing/seeing if it was in the car")? I hear it all the time from my immediate family, but I've never been able to find it referenced beyond that.
It is fading, and it hasn't been in widespread use for quite some time. However when I was in the UK, I definitely heard "tha" and "thissen" (yourself) on numerous occasions, mostly in common idioms and phrases, in South Yorkshire, especially around Barnsley and Rotherham. I don't think I ever heard it in major metropolitan areas like Manchester or Liverpool though.
You're more likely thinking of Quakers. At least those still a part of the mid-Atlantic tradition historically use "thou" to avoid power distinctions. Not many still do this in daily speech, but it's not absolutely lost, and is sometimes used for emphasis in a conversation in which matters of power and equality are lurking.
I think Thee would be for family, friends, or someone of equal social status and thou is more formal (but much less used now - only as tha: “tha's gonna get it“).
Old Yorkshire phrase for telling children to mind who they address as 'thee / tha': "Don't thee tha them as thas thee" - kind of a similar sense as 'mind your Ps and Qs'.