In discussing new usage problems discussed on the internet, Hielke Vriesendorp recently noted that there/their/they’re spellings were among the five most commented upon features listed in a Facebook group survey he carried out. Reading an early 17th-century text for the course Early Modern Everyday English which I’m teaching, one of my students spotted a similar error in a tailor’s account for three dresses he made for Sir Robert Spencer’s daughters:
iiij s for lace to binde all there bodies [bodices] and for sowinge silcke
The writer, a tailor called Richard Warwick, is literate enough (as well as numerate, an important requirement to be able to make up accounts like this), so it may have been a simple oversight. It happens to us all any time as well. Very well spotted, Joyce!
Bridging the Unbridgeable 
This is interesting. Gilman (1989) has an entry on “Their, there, they’re” under “their”, where he says “Haste and inattention to detail probably have more to do with most such errors than does actual confusion” (p. 897). Garner (2016) has it as “an embarrassing confusion of homophones … one expects from a grade-school student …” (p. 905). Butterfield (2015) says that “their” “is to be carefully distinguished from ‘there’ … and ‘they’re’ …” (p. 811). Peters (2004) doesn’t seem to mention it. I could find no mention of “there” `as an alternative spelling of “their” in the OED online. Does this mean that this has always been regarded as an error, and never as a variant? Does this make it unusual?
If I may just finish with another quotation from Garner (2016) on “their” and “they’re”: “A book like this one need not explain such elementary distinctions.”
References
Butterfield, J (2015, fourth edition) Fowler’s dictionary of modern English usage. Oxford University Press.
Garner, B A (2016, fourth edition) Garner’s modern English usage. Oxford University Press.
Gilman, E W (ed) (1989) Webster’s dictionary of English usage. Merriam-Webster.
Peters, P (2004) The Cambridge guide to English Usage. Cambridge University Press