This film was released in 2002 and SIX YEARS had passed since the second movie from 1996. The first two movies portray the family as they were in the LATER seasons of the TV series (season 4 & 5 era), so all the actors except the parents and Alice would be too old to reprise those roles in 2002. There was only two things they could do: have the third film parody older Brady's (like make fun of The Brady Bunch Variety Hour when Bobby & Cindy were teens and they had a "fake Jan") OR recast with younger actors and portray the Brady's during an earlier time in the TV series.

The latter scenario appears to the option they went with. Especially with Peter, Cindy, and Bobby, you can tell they're noticeably YOUNGER characters than the first two films. "The Brady Bunch in the White House" is probably chronologically occurring about three years BEFORE the first movie, so its the Brady's as they were c. season 2 of the TV series. Notice how Cindy looks like season 2 Cindy but in "The Brady Bunch Movie" and "A Very Brady Sequel", she looks like season 5 Cindy.

The only thing that's off is that Mike and Carol are obviously older than they were in the first two, and they didn't make any attempt to similarly regress their appearance to season 2 Mike and Carol. He still has the afro from season 5.