Both of my cats were with me long before my two reptiles. They are in their mid to late age with very different personalities. Isis ss very chill, inquisitive, but knows her limits and doesn't take risks. When I first introduced her to the Hermes (who was full grown by then), she wasn't sure what to make of him. She sat, at a distance, staring at this short spiney thing that randomly moved. During one brave moment, she lifted up a paw, slightly extended it as if to touch Hermes, before changing her mind and setting the paw back to the floor. Bravado is not with this one. She does, however, really like laying inside Hermes enclosure since it's so warm. There was one time I had one of the plexiglass doors slid open so she took the liberty to jump into the enclosure with the lizard while my back was turned. Usually she sleeps on top (the enclosure is one of those crossfire types), but this time she an opportunity to explore the inside. I turn to find her curled up inside the tank, the reptile looking extremely confused, as she hunkered down to sleep on the warm side. Obviously I wasn't going to let her do this. She still, rarely, tries to get inside the cage but I stop her before she makes progress. She's also hopped up on Sienna's cage which does have the mesh top, but in Isises old age, I think she simply prefers to sleep all day on my bed. She's not the one I'm worried about though.
Murphy is. He has a lot of jealousy issues and can be very defensive. I'd wager this has a lot to do with when Hermes would just crawl over the cat to get from point A to point B and Murphy started getting anxious about this. He would also try and bat both Sienna and Hermes heads if they did something Murphy didn't like. Like licking him or mistaking a whisker as food. He's one I have to keep a close eye on.
This is all going to depend on the personality of the cat. Some get along swimmingly with other animals, others can have their issues. I never leave my dragons unsupervised when they are out; they are either in my lap or on the floor and watched with eagle eye if Murphy is in the room. I cannot trust that cat fully. Some day's he's great, others not so much. Getting the cat used to the reptile will be a slow process. I allowed Hermes and the cats to mingle in small increments. If either one of the cats seemed upset, the reptile went back in the cage.