First thoughts are it's a bad idea to cut through the stile and panel. I normally never suggest changing a door but in this case if you kept the original one and got one purpose made to contain a catflap you could at least change it back easily if you needed to.
A picture would help to assess the type of stile/rail/panel construction then it might be possible to give better advise. I'm guessing if you really need to go ahead with it sticking a thin panel to the butchered door with epoxy resin would allow you to even out the difference in thickness between rail and panel and fill the gap left by the moulding.
Here's the door, inside and out. I've taped on the frame outside at the lowest height it could be without straddling the moulding. The exterior is covered and on a protected side of the house so I don't have to worry too much about weather proofing, but it does get cold.
Really can't think of any way to help you decide. Fire door blank and keep the old door would probably be better than butchering that one. I would expect a cat to be able to get in and out of a cat flap where you have it taped now though, unless it's particularly small.
First thoughts are it's a bad idea to cut through the stile and panel. I normally never suggest changing a door but in this case if you kept the original one and got one purpose made to contain a catflap you could at least change it back easily if you needed to.
A picture would help to assess the type of stile/rail/panel construction then it might be possible to give better advise. I'm guessing if you really need to go ahead with it sticking a thin panel to the butchered door with epoxy resin would allow you to even out the difference in thickness between rail and panel and fill the gap left by the moulding.