Suppose i have an output of tourism of 4 and someone else has 6.
As mp wrote, relative tourism output is not relevant. There is no direct game effect from that.
I would not have thought that ideology pressure was so vexing at King. I know I frequently struggle with it at Deity. OP, you write that you delay Ideologies so as to go with the flow. I would think that works pretty well, and I use that tactic sometimes as well, but the game seems like less fun that way. Some games, I have a particular VC in mind, so in those cases I really want to be first to Freedom or Autocracy. However, my usual preferred approach is to rush Ideologies, get to Order first (since the AIs seem to prefer it), and then beeline Railroads to build Kremlin (since it is unlocked earlier than Prora or SoL).
At that point, I can decide to ride things out or switch (right after unlocking an SP, so as not to lose much culture). It feels like win/win since, even if I do switch, (1) I am up one free SP, and (2) I prefer both Freedom and Autocracy to Order anyway! Building Kremlin is pretty reliable in my play, and when I do switch, in about half my games I can still snag Prora or SoL (so two free SP net, even with switching).
If you are never going to catch them up but they are very close to catching your culture score then I would cancel the open borders and find other civs to trade with, as you are just helping them win.
It may not really be helping them win (since at King they have little chance of any VC) but it is helping them exert Ideology pressure on you. You can close your borders and buy open borders from them for as little as 2gpt.
That feels cheesy to me, so I hardly ever do that. I get the impression that one-way open borders is a pretty common technique.