Should you use "who" or "that" when talking about multiple people doing something?

Which of the following is correct?

• There were 10 people that went to the store.
• There were 10 people who went to the store.

Edit:

Which of the following is correct?

• There were 10 people that had brown hair.
• There were 10 people who had brown hair.

Solution 1:

• There were 10 people who went to the store.
• There were 10 people who had brown hair.

Who refers to people. That and which refer to groups or things. (grammarbook)

Solution 2:

They are interchangeable.

http://www.merriam-webster.com/dictionary/that

1 a : the person, thing, or idea indicated, mentioned, or understood from the situation b : the time, action, or event specified c : the kind or thing specified as follows d : one or a group of the indicated kind

Beware of grammar books. They very often describe the authors' opinions on what grammar should be, rather than what grammar actually is.

Specifically, I would say that it is fine to use either "that" or "who", but "who" can only be used to refer to people, while "that" refers to things and people. One should favour the word "who", if they want to clarify that it is a person, and not a thing, that they are talking about.

Jean Yates says in her book, "The Ins and Outs of Prepositions":

An adjective clause can identify a noun. The clause comes right after the noun.
...
TO IDENTIFY A PERSON, AN ADJECTIVE CLAUSE CAN BEGIN WITH WHO(M), THAT,
...
The man who(m) ...
The man that ....
...
The people who(m) ...
The people that ...

Furthermore, the "Longman Student Grammar of Spoken and Written English" by Douglas Biber, Susan Conrad, and Geoffrey Leech says:

Three relative pronouns stand out as being particularly common in English: who, which, and that.
...

• That and zero are the preferred choices in conversation, although relative clauses are generally rare in that register.
• Fiction is similar to conversation in its preference for that.
• In contrast, news shows a much stronger preference for which and who, and academic prose strongly prefers which.

So again, I say, be wary of any single grammar book as being 100% correct. They never are.

Solution 3:

It's worth noting that the term "who" with a preceding comma often has a different meaning from "that", and the latter term would not substitute. Consider:

1. The six friends, who had gone to school together, went to the beach.
2. The six friends that had gone to school together went to the beach.

In the first sentence, it is assumed that the reader would know, even before reading the italicized portion of the text, what the six friends the author was referring to, but not that they had gone to school together. In the second sentence, it is assumed that the reader would know that six friends had gone to school together, but not that the author was writing about those people in particular.

When discussing inanimate objects, the word "who" in the first usage above would be replaced with "which". Replacing the word "that" in the second usage with "who" would be reasonably common usage when discussing people, but comparable replacement with "which" would be less common, especially when the subordinate clause modifies the subject of a sentence. "The six machines which weren't working this morning have been repaired" would read slightly less naturally than "The six machines that weren't working this morning...", though "I have fixed the six machines which weren't working this morning" would be fine.