LOL. I built a cage for my GF's Bearded Dragon and she nixed the idea of weather stripping for the same reason.
Three ideas:
1) Figure out how big your gap is and have a slightly thinner acrylic strip cut. How thick the strip needs to be will depend on what brand of glass track you have and exactly how thick your acrylic is (some 1/4" acrylic is actually 6 mm or 3/16"
.
Use a very small amount of solvent to attach this strip to the end of one of your acrylic panels. If the solvent welded area looks bad then cover the whole are with a thin strip of attractive wood. This will double as a finger pull of sorts.
2) Use the weather stripping inbetween the panels and cover the area with a piece of wood as described above.
3) Buy a piece of quarter round and route a dado along the back. The dado will be the same depth as the thickness of the acrylic. Attach a piece of adhesive backed weather stripping to the part of the quarter round that hangs over the edge.
Choice #1 has the great chance of maintaining a clean look, but is also the most likely to scratch up your panels due to acrylic rubbing on acrylic.
Weather stripping can also put fine scratches in acrylic but these will be easier to buff out. Due to that I like choices 2 or 3. Choice #3 is a bit more difficult but would by my preference.