David Yoho
Your best solution would be to finish first. However, if for some reason it's not possible in this case, blue painter's tape and liquid hide glue is the next best approach.

I found out not all blue tape is equal. I look for the 3M brand with an orange colored core. Carefully applied along the mitered edges, it will provide acceptable protection. Any hide glue squeeze-out will dry hard and is easy to remove with a sharp chisel and a little hot water wipe. If a little does stay in the wood it tends to hide better under finish than yellow glue.