This is a fairly simple request, but it would be a huge quality of life improvement to be able to disable pet interactions. Allow me to explain.
I love the pets. I love having them around. I love the way they dance, follow me, and nibble on food I hold out.
What I don't love is when I'm trying to grab my wheel or sail in the middle of combat and I end up picking up my pet and smashing into a rock instead, or picking up the pet of an enemy player nearby while I'm trying to use a barrel quickly.
In short, pets are great, but their 'pick up' interaction means that I never want to have them out, since they'll always interfere with emergent PVP combat at a critical moment, and it's never fun to lose a fight that way.
