Nice looking gate, I can see why you like it. I’m guessing (yes only guessing) that the lionhead would be able to get thru, maybe even the angora. I would be a little afraid of them just being able to get their heads through the bars. If they moved too fast, they could possibly hurt themselves freeing themselves from it.
I haven’t done any gate searching myself, so don’t know all the available styles or costs, but… if -I- had decided that this was THE GATE I HAD TO HAVE… I would probably do some modification to it to ensure they couldn’t get their heads through. The spacing on the bars on my xpen are 1.5″ and my holland lop can’t put his head thru it. He CAN get half his face thru it, up to his eyeballs.
Your wood floors are lovely! I’m guessing this gate appeals to you because it has the design that is not only functional but also attractive to the eye. So I’m not sure if any ideas of modifying would take that appeal away or not. I would consider things like NIC grids zip-tied to it or maybe even something like weaving flexible clear-sheeting thru it, so you could still see thru it.