You're comparing a string to a symbol, you probably want to write:
- if request.subdomain == 'admin'
-if utility == "delete"
%button.delete
Your render syntax is also a bit off, instead of:
= render 'admin/projects', locals: { utility: "delete" }
Use
= render :partial => 'admin/projects', locals: { utility: "delete" }
I answered a similar question earlier here: Rails asking for a secret key to create model