>>717758762
It's never stopped them really. They just pay their respects normally.
Special Week for reference passed away a short while after the anime originally started airing.
If anything, when season 2 was airing there was a minor commotion over new fans paying their respects to Rice Shower's grave by placing flowers that were considered disrespectful to the real horse by older keiba fans, but it never escalated into a huge problem.