"Here Comes the Bride" (a. k. a. "The Bridal Chorus"), often used as a wedding processional, is from Richard Wagner's Lohengren.
The Wedding March, often used as a recessional, is from Felix Mendelssohn's incidental music for A Midsummer Night's Dream.
The irony is of the juxtaposition of Mendelssohn</a>, born to Jewish parents (who, in the interests of assimilation, had him baptized in the Lutheran church) and the famously anti-Semitic Wagner in wedding ceremonies ever since Princess Victoria selected the two pieces for her marriage to Prince Friedrich Wilhelm on January 25, 1858.
Apparently Wagner even singled out Mendelssohn and his work, although when his article "Das Judenthum in der Musik" came out in 1850 it was published under a pseudonym, and it is not clear to me whether at the date of the wedding these views were well known.
At any rate, this is not a comment on whether either of these pieces should or shouldn't be played at a wedding, or on whether the personal lives of composers should affect how people feel about their work. It's agreed that both were great composers who wrote some fine music.
These two pieces have become such a traditional pairing, and yet I see a remarkable irony in having them played together.
HRH Princess Victoria, The Princess Royal was the daughter of Queen Victoria of Great Britain. Later, her son became Kaiser Wilhelm II.
HRH Prince Friedrich Wilhelm of Prussia became Kaiser Friedrich III of Germany but only reigned for 99 days before dying of cancer of the larnyx. He was then succeeded by his son, Wilhelm II.