How do I prioritize my textures in a realm?

My problem is that when I enter a realm (which has its own textures), my textures don't usually appear. Right, I already knew that, and probably everyone here does too, but that's not my issue.

The problem I'm having is this: even though the realm has its own textures and add-ons, sometimes it does let me use my textures. I always have my textures enabled, and sometimes it lets me use them (very rarely), and other times it doesn't, and it's in the same realm.

So I'm wondering, how does this work? If it lets me in sometimes, is there any way to manipulate this so I can always use my textures?