A topic from AEG's L5R CCG Rules forum, copied for Oracle of the Void from a copy of the forum saved in October 2015, so pages it didn't save are missing. Players' names are left out; the rules officials are named. Rulings are as they stood on these dates; later rulings, the rulebooks and the Rules Archive may differ.
Bayushi Toshimo: Battle: Target an enemy card without attachments: Bow it. If Toshimo has a Weapon or you control a Courtier, negate the card's straightening.
Vigilant Riders: After this card bows: Straighten it. Reaction: After another player's action targets a card in this unit: Negate this card's destruction from the action's effects.
Would Toshimo's ability cancel the Rider's Trait?
Bayushi Toshimo: Battle: Target an enemy card without attachments: Bow it. If Toshimo has a Weapon or you control a Courtier, negate the card's straightening.
Vigilant Riders: After this card bows: Straighten it. Reaction: After another player's action targets a card in this unit: Negate this card's destruction from the action's effects.
Would Toshimo's ability cancel the Rider's Trait?
"Sort of".
Effects resolve sequentially. Therefore, in this case:
1. Toshimo's action bows the Vigilant Riders 2. The Vigilant Riders immediately straighten per their trait 3. Toshimo's negation of straightening effect kicks in
If you were to then bow the Riders again that turn, they would not straighten.