Not at all implausible, I'd say. The really strange thing, from a
history of ideas perspective, is that the English parliament outlawed
Christmas because it was seen as either "too papist" or "too pagan"
(without necessarily distinguishing too much between these).
But historically (and at that time, that meant less than a century ago)
it had been Martin Luther who had more or less invented the modern
idea of Christmas, at least in northern and Central Europe. Prior to that,
the main day of Festivities had been December 6th, St Nicolaus day,
the 25th was pretty much irrelevant.
The early church didn't celebrate it either, indeed, there was widespread
disagreement regarding the date - March 28, April 2, April 19,
May 20, November 17 all had some backing by early patristic writers,
and in some Christian denominations it's still today the 6.1. And
unlike the question of when to date Easter, where different dates lead to schisms and
persecution, nobody got their hackles up over the birthday. It was deemed
theologically irrelevant.
Luther now was concerned over what he saw as "pagan" St.Nicolaus
celebrations, the festivities and the gift giving in particular, so he promoted
the 25th as an alternative, to refocus from a Saint to the person of Christ.
Confused? You will be, because after that it gets really complicated: In
Luther's admonitions, the focus on St Nicholas is replaced to
one on the "Heiliger Christ" (Holy Christ), but for him there was no link to Jesus
as a baby, and definitely no nativity plays etc. His "Heilige Christ"
however transmogrified quickly into two competing version,
the "Christkind" (Christmas child - not Christ, but a sort of gift
bringing angel) and the "Weihnachtsmann" (Christmas man) -
the latter dominating Northern and Eastern Germany.
And then finally in the 19th century, the Victorians merge back the
Weihnachtsman with the original St Nicolaus celebrations, giving
us Santa Claus etc
So when the English Parliament started its war against Christmas
out of anti-catholic sentiment, they really attacked a practice
that owed more to Luther than the Pope. As another historical
oddity, while in England these laws were soon revoked, their cultural
impact remained strongest outside England, in Scotland. As recent as
the 1980s and early 90s, Christmas was really not a "thing" up here,
people saved up their energy and money for Hogmany. It is mainly a
result of the pressures of global capitalism and its advertising budgets
that that has changed by now.