TL/DR: Don't worry about the alcohol thing; pick a finish that's easy to use.
What finish can I use that will be indoors and likely will be in
contact with alcoholic liquids?
I hate to write an answer that doesn't answer your specific question, but I think you're focusing on the wrong thing here. The finish that's best known for being susceptible to damage from alcohol is shellac, and that's because alcohol is a solvent for shellac. But even shellac won't be instantly and irreversible damaged by the amount of alcohol in wine, and repairing a shellac finish is relatively simple.
In reality, almost any finish could work for a wine rack. Given that, you should look for a finish that matches your experience level. Look for finishes with the following characteristics:
Start by learning a little about the various types of finishes. Here's a video from finewoodworking.com that covers the very basics. As you'll see in the video, there are a number of finishes out there where you just wipe the finish onto your project with a rag and then wipe off the excess. These types of finishes usually dry quickly and tend to be very forgiving: if you missed a spot or want to even the finish out, you can apply more; if you want to change the look, you can rub it down with steel wool or a soft rag.
Toxicity isn't usually a big concern except when you're applying finishes (you need to watch out especially for fumes from solvents). Dried/cured finishes are generally safe for most uses, and no finish materials are going to get through a wine bottle. But since you mentioned it, you might want to take a look at the finishes from Tried & True. These are all in the easy/fast/cheap/attractive category. I used the Varnish Oil on a side table I built a dozen years ago, and it continues to look great.
Finally, go with your gut. Every woodworker has his or her own favorite finish. In fact, many will talk about a finishing schedule, i.e. a whole list of finishing steps required to achieve their favorite look. The even-numbered steps generally involve application of some potion or other, and the odd-numbered steps call for application of elbow grease and some form of abrasive material. Don't be intimidated by all that -- you can get a very nice finish by just sanding, applying a single potion as described above, and optionally buffing with a cloth and maybe a touch of wax.