Are Germans afraid to use the word "Weihnachtsmarkt" (Christmas market) and therefore use "Lichtermarkt" (market of lights) or "Märchenmarkt" (fairy tale market) so as not to offend Muslims living in the country by using an expression referring to Christian religion? No, that's not true: Even cities used the word Christmas market on their official websites in December 2023 to publicize these events as an attraction for the population and for tourists.
The claim appeared in a video (archived here) on TikTok on December 20, 2023. It said (translated from Hungarian to English by Lead Stories staff):
In many places in Germany, people no longer dare to call the stalls offering food and drink before the festive season a Christmas market; instead, the event has to be referred to as a market of lights or a fairy tale market. So as not to offend the feelings of the many Muslims in Germany.
This is what the post looked like on TikTok at the time of writing:
(Source: TikTok screenshot taken on Wed Dec 27 15:19:33 2023 UTC)
A Google search conducted by Lead Stories using the word "Weihnachtsmarkt" (archived here) resulted in many official websites that use this term. The official website of the city Berlin, for example, calls the markets "Weihnachtsmarkt" and lists almost 100 such events in the city. Sixty of the events have the word "Weihnacht" (Christmas) in their title, while there are three markets of lights and zero fairy tale markets. Germany's second-largest city, Hamburg, also uses the word "Weihnachtsmarkt" on its website and listed several of them in the city for the 2023 season.
The source of the claim in the video is unclear. Several posts with the same claim also appeared on Facebook in Hungarian, such as here (archived here). None of them named a source. The right-wing German party Alternative für Deutschland published a statement with the same claim in 2017. Although it has disappeared from the website, the archived link can be found here.