As with it parent series, Happy Days, the main characters of Joanie Loves Chachi had hairstyles and fashion tastes more appropriate for the early 1980s than for the early 1960s. In later episodes of the series, clothing obviously made of synthetic materials managed to creep in, even though it was a decade or so (the early 1970s) when such materials would become popular.
Given the moderate to conservative nature of the Cunningham family it's doubtful that the would have approved of their single daughter moving away with a man, regardless of who he was, without the two being married. While this may have been acceptable in the 1980s era when it was filmed, it would have been viewed as completely inappropriate in the early 1960s setting of the series.
The social mores and values in the series more clearly reflected the 1980s filming period of the series rather than its 1960s setting. Smoking was largely eschewed, women were treated as equals and ethnic White Americans were not disparaged as they were during the early 1960s when the series was set.