I have come across several people who have locked all their pets and write in their trade rules that they're not trading. It's perfectly fine if they're not up for it, but it would be easier for them to just be able to toggle trades on or off instead of having to lock all their groups.
If someone has trades toggled off, the trade button does not appear at all. This would help users of both parties:
1. Not seeing a trade button could save a trader from having to navigate a trade page.
2. Someone with trades turned off doesn't have to worry about locking all their groups and then having to unlock them again when they want to trade.
I wouldn't see this suggestion as a massive priority, but something to keep on the back burner. We already have a way to lock C$ and items from trades, why not pets too, or just trade altogether?