MetaMask is for sending simple transactions and exposing Ethereum API into the DOM so that web-applications can be more easily developed for Ethereum. It is not capable of executing smart contracts directly.
That said, it doesn't matter what wallet you're using for this step. The only thing required here is your Ethereum address, it's a constant, or read only function.
You would have to get private key from metamask and login to Myetherwallet with the private key to do it. Which is not recommended way to login to a website.
MetaMask is for sending simple transactions and exposing Ethereum API into the DOM so that web-applications can be more easily developed for Ethereum. It is not capable of executing smart contracts directly.
That said, it doesn't matter what wallet you're using for this step. The only thing required here is your Ethereum address, it's a constant, or read only function.
You would have to get private key from metamask and login to Myetherwallet with the private key to do it. Which is not recommended way to login to a website.