How to create reusable Azure devops Yaml template not coupled to GIT

As @4c74356b41 mentioned there is nothing bad to keeping coupling to git. There is no other better way than keeping YAML template than in git repo. If you have sth common across project or organization, create separate repo just for templates. And yes you can point to specific template in that repo. Please take a look here

If you have repo Contoso/BuildTemplates and `common.yml' there

# Repo: Contoso/BuildTemplates
# File: common.yml
parameters:
- name: 'vmImage'
  default: 'ubuntu 16.04'
  type: string

jobs:
- job: Build
  pool:
    vmImage: ${{ parameters.vmImage }}
  steps:
  - script: npm install
  - script: npm test

you can refer to this template in another repo like this:

# Repo: Contoso/LinuxProduct
# File: azure-pipelines.yml
resources:
  repositories:
    - repository: templates
      type: github
      name: Contoso/BuildTemplates

jobs:
- template: common.yml@templates  # Template reference

where common.yml is name of the template and templates is alias for your repo where you keep templates.