Is it reasonable to assume that designers should know how to use git
I would say no, especially if their coding starts and ends just at HTML. Unless you are directly hiring for these "checkbox skills" then it isn't reasonable to assume that they would have these skills. This question should be brought up in the hiring phase since your workflow hinges on it.
I'm wondering what kind of dev environment and tools are reasonable
for web designers?
Slack, FTP Clients, Web to Print Portals, Sketch, Dreamweaver, JQuery, Ruby on Rails and Angular come to mind. It really depends on the type of webdev being done and the job requirements. Webdev is such a fast changing landscape so it's hard to say what will be "trendy" or essential with much certainty.
We've hired someone who is familiar with css and html but not really
git, github, the command line.
We could obviously train this person, but I'm wondering if we should
YOU SHOULD 100% TRAIN THEM!
Seriously. If you are even considering not teaching your company's workflow and programs, you are setting yourself up for failure. Not all workflows are taught or know beforehand and they are usually unique to each company. Yes there's some crossover but not having a new person onboard from the get-go is like just handing car keys over to a 10 year old and just letting them lose.
I'm wondering how the workflow would operate if we didn't get this
person using git.
I don't know, only you can answer that, you haven't given enough detail on your daily operation. My recommendation is train them asap but work with your management to set-up a stop-gap workflow that a person can be started in while they are getting acclimated to the primary workflow.
Say, they would sftp to a remote server where they would work and then when they're ready, another person could do the git stuff?
What do you guys do?
It depends on the job, but I work locally and then we use IBM Watson automation along with some other online marketing services like Sales Force. It really all comes down to the client, your resources and what works for you.
There is no catch-all method for everyone.