In the show the Last Kingdom, the Anglo-Saxon priest Father Beocca gets legally married to a Dane named Thyra. It is to my understanding that priests are expected to be celibate. Are there any instances of this happening in the past, or is this just a creative liberty the show decided to take? Did Church doctrine used to be more lenient, or did some people just ignore it?
The short answer to your question is yes, this sort of thing did happen.
The church at this time did officially teach against clerical marriage, but clergy discipline on this issue was lax. Earlier in the medieval period, popes were very limited in their ability to enforce these kinds of rules, and how rigorously they were applied depended quite heavily on the willingness of local authorities, which was not always forthcoming. It was not at all uncommon, especially for priests in more remote areas, to marry or to live openly with concubines. We know this because we have documentation about complaints to this effect, and documents including the Northumbrian Priests Law and penitential texts indicate that this was occurring. Under the letter of canon law, these kinds of arrangements were not permitted, but enforcement was difficult and inconsistent. Historian Kevin Madigan suggests that this was common throughout the Latin West: "Simply put, virtually no rural parishioner or priest in the year 1000 regarded clerical concubinage or marriage as practically or canonically objectionable; it would be more than a century before this would change and we begin to have evidence of reforming by lay groups demanding clerical celibacy." (Madigan, Medieval Christianity: A New History, p. 84).
Readings
Kevin Madigan, Medieval Christianity: A New History
Joseph Lynch, Christianizing Kinship: Ritual Sponsorship in Anglo-Saxon England
C. N. L. Brooke, "Gregorian Reform in Action: Clerical Marriage in England, 1050 - 1200"
Margaret Clunies Ross, "Concubinage in Anglo-Saxon England"