Concrete is vulnerable to etching and staining from anything acidic like lemon juice, vinegar, red wine, etc.
Sealing isn't necessary but it will help protect the concrete from staining and keep them looking nice for a long time.
Check out the Sealing Concrete Countertops + More Instructable for tips on applying CHENG Sealer.
If your coasters don't sit flat, you can cut thin cork backs or little cork feet and attach them with spray adhesive.
Hopefully this little project will inspire you to make something concrete. Thanks for following.