[kafkaesq]

Apparently, the "certainly implement" part was a misattribution. But if you follow the analysis in the article you posted, it's quite clear that Trump basically does favor the idea of such a registry -- and that yes, it would be mandatory for all "legal" entries into the country:

Friday, Nov. 20

The next day, an MSNBC reporter asked Trump, "Should there be a database or system that tracks Muslims in this country?"

"There should be a lot of systems," Trump responded. "Beyond databases. I mean, we should have a lot of systems."

Trump then digressed to talk about a wall along the southern border, before the reporter interjected, "But that’s something your White House would like to implement."

"I would certainly implement that. Absolutely," Trump said.

Here, we’re not clear if Trump is talking about implementing a wall or implementing a database.

But a few seconds later, when asked how he would register people into a database, Trump said, "It would just be good management."

Finally, the reporter asked if Muslims would legally have to be part of the database.

"They have to be — they have to be," Trump said. "Let me just tell you: The key is people can come to the country, but they have to come legally."

[fib739mbbh]

I'm not sure what you specifically mean by "such a registry", but if you read further, he clarifies his comments to MSNBC by saying he means a registry for Syrian refugees.

After Trump’s tweet, Fox News asked him about his position on a Muslim registry.

"Let's hear it directly from you," said host Kimberly Guilfoyle. "Would President Donald Trump support a full Muslim database?"

"Basically the suggestion was made and (it’s) certainly something we should start thinking about," Trump said, repeating that the reporter presented the idea. "But what I want is a watch list. I want surveillance programs. Obviously, there are a lot of problems. … But, certainly, I would want to have a database for the refugees, for the Syrian refugees that are coming in because nobody knows where they're coming from."

Guilfoyle followed up: "So to be clear, you are not saying anything with respect to a religious database. You are talking about the Syrian refugees in light of the national security development affecting this country as we speak here tonight."

Trump said he didn’t hear the MSNBC reporter’s question clearly, "but even if I did, I mean, I want databases for the Syrian refugees that Obama is going to let in if they come in."

[kafkaesq]

Taken together, the best spin you can put on these statements is that he's obviously too muddle-headed to be shouldered with the responsibility of formulating and articulating national policy on sensitive issues like these.

[ams6110]

All legal aliens in this country are already in a database. They have green cards or are here on some sort of visa, and it's all tracked in databases. All citizens are as well, unless they are young enough or isolated enough to never have had a job or a credit card or filed a tax return or had any other interaction with the governemnt.