Depends on the house plants and it depends on the cat. Unfortunately that's not a great answer for you. You won't know how the cat will react (some always chew on plants, some do only occasionally and some never do)
But you can take the time to research each one of your houseplants which is tedious but at least with photo apps, there's a lot of plant identification apps out there that can be correct more than they're incorrect...
The problem is the cats are very different and almost everything is toxic to them. They can also be very curious and although chewing on a plant usually the worst thing that will happen is that they'll have vomiting or diarrhea, in some cases it can actually be fatal and even the first time.
So what you going to have to do is identify your plants. It is possible that some of your plants can be rearranged in places that are way too high for a cat (although never underestimate a cat, plus, it is always possible that they could drop a flower or a leaf or something else that the cat could possibly then find on the ground)
I have probably at least 50 houseplants of which there are at least 30 different types, and most of these are in some way shape or form toxic to cats. And yet I have three cats. I have arranged mine so that they are most dangerous in the least accessible area, and least dangerous closer to the ground. This isn't perfect, But my cats also seem to show no inclination to not on plants and I've had the cats and plants in the same house for 8 years with no problem.
But to be safe, yes, you should get rid of any plants that's considered to be toxic to cats. Which of course sucks for you because obviously you enjoy your plants.
Hope this helps, and I hope that you do decide to adopt a cat and that you will find the love and comfort of the cat will far outweigh the displeasure you might feel at having to rehome a few houseplants