"strongly" or "strong"?

Solution 1:

Both are correct, but strong is a bit better.

• Strong Protestant and unionist identity says that the 36th Division had a Protestant and unionist identity, and that sense of collective identity was intense.

• Strongly Protestant and unionist identity says that the 36th Division had a sense of identity, and that identity was intensely Protestant and unionist in character.

The difference is subtle. I think both statements are accurate, but the former is closer to what the article means to say. So strong is the right word to use.

Martha says that strong Protestant and unionist identity is strictly speaking incorrect unless you add commas. I disagree. It’s completely standard. It is easy to find plenty of examples of this pattern in good journalism and academic writing. Here are some examples (found in the Corpus of Contemporary American English):

strong economic and political ties

a strong moral and ethical impulse

an Iranian culture with strong Hellenistic and Indian traditions

complex social and economic conditions

overall physical and mental health

alternating hot and cold water

There are thousands more. The pattern also appears in the name of the National Oceanic and Atmospheric Administration, a U.S. government agency.

Solution 2:

"Strongly" is okay in this sentence. To help clarify:

It had a [strongly Protestant and unionist] identity.

"Strongly" is modifying "Protestant and unionist" to compare it against a mildly Protestant/union identity. Using "strong" would change the meaning and require some fiddling:

It had a strong, Protestant, unionist identity.

Here, we could remove the last two adjectives:

It had a strong identity.

The possible source of confusion is the "and" between "Protestant" and "unionist":

It had a strongly Protestant identity.

This probably sounds less awkward.

Solution 3:

Strongly is correct. In grammatical terms, strongly is an adverb modifying, in this case, the adjectives Protestant and unionist, which are in turn modifying the noun identity.

There is a tendency in modern English to use adjectives as adverbs, resulting in things like "... a strong Protestant and unionist identity...", but strictly speaking this is incorrect, unless you add commas to make the adjective modify the noun instead: "... a strong, Protestant, and unionist identity..." — but obviously the latter means something quite different than the version without commas.

That said, unless you're writing for a particularly nitpicky audience, either choice is fine and will be understood as an adverb (unless marked as an adjective).