In the past I have cut the acrylic to size using my Bosch plunge router and guides, and either made templates or set up straight guides to do the cutouts and ensure perfectly square/straight lines. To do this more efficiently I thought I would try a router table...
You can use a template with the router table to do the straight lines. Your router table should have come with a guide pin you can screw into the baseplate. Use that instead of the fence, and make sure not to get your fingers too close to the spinning bit.
Having never used the table before, I wanted to be clear on general safety. One of the things I’ve read is you should never have your work piece sandwiched between the fence and bit. I was planning on doing just that to “rip” the acrylic to size (ie set fence at 7” to cut the overall rectangle from a larger piece of acrylic), and again have a portion of the acrylic between the bit and fence as I wanted to use the fence as my straight edge to make the cutouts.
It's correct that is not a good idea to make a through cut where the workpiece can be pinched between the fence and bit. However, you could firmly tape the face of the acrylic to a sacrificial piece of wood using double-sided tape. If you only cut slightly into the wood on your last pass on the router table, you are not making a through cut and your chance of kickback is reduced. For even greater safety, you could use a spacer to offset the acrylic from the edge of the wood. This way, the wood runs against the fence, while the acrylic is set away from the fence by a consistent space, and won't have an opportunity to be pinched between the bit and fence.
I guess what I’m wondering is, whether the router table is the right tool for this job.
I hate to say it, but for the straight cuts you don't even need a power tool. You can score the acrylic several times on each side using a straightedge and sharp utility knife, then snap the acrylic along the score line. In fact, depending where you buy your material, they may cut it to size for you using exactly this method.
None of this necessarily means the router table is the wrong tool for the job. It just means that there are many ways to achieve what you want, and for safety's sake, you will need to make some minor tweaks to how you thought you would use your router table.