To create a Mermaid diagram that represents the relationships mappings of all entities in a microservices architecture with a React frontend and REST API backends accessed via a Mule gateway, we would represent each component (React frontend, Mule gateway, and each microservice) as a node and then illustrate the relationships between them. Below is an example of what this diagram could look like in Mermaid code:

mermaid
graph LR
  ReactFrontend[React Frontend] --> MuleGateway[Mule API Gateway]

  MuleGateway --> UserMicroservice[User Service]
  MuleGateway --> OrdersMicroservice[Orders Service]
  MuleGateway --> InventoryMicroservice[Inventory Service]
  MuleGateway --> PaymentMicroservice[Payment Service]

  UserMicroservice --> UserDB[(User Database)]
  OrdersMicroservice --> OrdersDB[(Orders Database)]
  InventoryMicroservice --> InventoryDB[(Inventory Database)]
  PaymentMicroservice --> PaymentDB[(Payment Database)]

  UserMicroservice --> |Read/Write| UserDB
  OrdersMicroservice --> |Read/Write| OrdersDB
  InventoryMicroservice --> |Read/Write| InventoryDB
  PaymentMicroservice --> |Read/Write| PaymentDB

  style ReactFrontend fill:#f9f,stroke:#333,stroke-width:4px
  style MuleGateway fill:#bbf,stroke:#f66,stroke-width:2px,stroke-dasharray: 5, 5
  style UserMicroservice fill:#ff9,stroke:#333,stroke-width:2px
  style OrdersMicroservice fill:#ff9,stroke:#333,stroke-width:2px
  style InventoryMicroservice fill:#ff9,stroke:#333,stroke-width:2px
  style PaymentMicroservice fill:#ff9,stroke:#333,stroke-width:2px
  style UserDB fill:#9f9,stroke:#333,stroke-width:2px
  style OrdersDB fill:#9f9,stroke:#333,stroke-width:2px
  style InventoryDB fill:#9f9,stroke:#333,stroke-width:2px
  style PaymentDB fill:#9f9,stroke:#333,stroke-width:2px

This code will generate a diagram with the React frontend communicating to the microservices through the Mule API gateway. Each microservice is connected to its corresponding database, and the type of interaction (Read/Write) is specified. The styling lines at the bottom are used to differentiate between different types of nodes (e.g., frontends, gateways, services, databases) with different colors and styles.