Adverb versus Adjective in -minded people
Solution 1:
According to the Collins English Dictionary,"-minded" combines with 3 parts of speech: adjectives, adverbs and nouns.
- "-minded" combines with adjectives to form words that describe someone's character, attitude, opinions, or intelligence: These are evil-minded people.
- "-minded" combines with adverbs to form adjectives that indicate that someone is interested in a particular subject or is able to think in a particular way: I am not an academically-minded person.
- "-minded" combines with nouns to form adjectives that indicate that someone thinks a particular thing is important or cares a lot about it: He is seen as more business-minded than his predecessor.
As for the hyphen, it should be used with the combining form "-minded".
Solution 2:
I started to address your question, but then realized it's actually more complicated than I had thought.
First, look at Oxford's definition of the adjective liberal-minded:
In early use: having a generous character or disposition. Later: holding liberal opinions; tolerant, broad-minded.
Now, look at its definition of the adverb liberally:
In large or generous amounts.
‘she quotes liberally from the Bible’
‘steaks liberally sprinkled with salt and pepper’
‘large firms contributed liberally to the relief fund’In a way that is not precise or strictly literal; loosely.
‘the law is interpreted liberally’
‘the obligations of treaties should be liberally construed’In a way that involves broadening a person's general knowledge and experience.
‘liberally educated students’In a way that favours individual liberty and moderate political and social reform.
‘I used to think more liberally’
A liberal-minded student student makes sense. But a liberally minded student seems a little odd. Depending on the sense of liberally, it may not mean exactly the same thing—or it may mean something strange.
I would say that, idiomatically, liberal-minded is what would normally be used.
As for artistic-minded student and artistically minded student, I would say that the reverse is true; that the use of the adverb is simply more common and, therefore, more natural.
There is no dictionary definition of the compound adjective artistic-minded that I can find. Without a dictionary definition, it becomes a constructed compound adjective.
I'd like to say that it sounds awkward and, therefore, nobody uses it—but that's not true.
A Google search turns up several uses of artistic-minded.
It's used in "A Visit to Ceylon" by George J. Romanes (emphasis mine):
We had, of course, read a good deal about Ceylon before, and thus knew that it was a part of the world which in point alike of natural scenery and natural history was well calculated to arouse the enthusiasm of such an artistic-minded naturalist as Prof. Haeckel; and knowing that his pen can paint almost as vividly as his brush, we were prepared for something of unusual interest in the story of his “Visit to Ceylon.”
It's used on the Centre Clark website (emphasis mine):
Following its initial mandate, CLARK has put forth numerous projects. Not only artistic-minded, but also community and educational as well. In parallel to its’ programming, it has completed several projects – both here and abroad.
So, I can't give a good answer as to why (besides rules of grammar that would indicate one or the other) sometimes the adjective is used and sometimes the adverb is used.
Although one form is likely more common, and that's the one that sounds more natural, it seems that it's just a matter of preference.
I can speak to the use of hyphens.
When forming a compound adjective, one where multiple adjectives are used in front of a noun, there is a series of guidelines that takes place.
Some compound adjectives are joined with a hyphen and others are not:
Here are some examples:
a five-year-old child
eighteen years of age
a second-best decision
he arrived fourth to last
The Chicago Manual of Style (17th ed.) has a hyphenation guide that is twelve-pages of nothing but specific examples and guidelines; and that's in addition to several other pages of general guidelines.
However, in general, that's why you see liberal-minded student but liberally minded student.
One specific rule from Chicago (7.86) talks about adverbs that end in ly:
Compounds formed by an adverb ending in ly plus an adjective or participle (such as largely irrelevant or smartly dressed) are not hyphenated either before or after a noun, since ambiguity is virtually impossible. (The ly ending with adverbs signals to the reader that the next word will be another modifier, not a noun.)
As I understand it, the majority of style guides and grammarians follow this guideline. That's why most recipes call for finely chopped onions and not finely-chopped onions.
Knowing this, I am at a loss to understand why Collins uses a hyphen in two example sentences formed by an ly adverb in its definition of -minded:
I am not an academically-minded person.
He was not mechanically-minded.
This goes against common stylistic rules, and doesn't match other dictionaries:
[Oxford's definition of scientifically]
‘scientifically minded people’
‘a scientifically important site’
[Your Dictionary's definition of scientifically]
In support of this belief there is more or less scientifically ascertained evidence
However, I can say with a fair degree of confidence that it's much more common to not use a hyphen in the constructions artistically minded students, scientifically minded students, and athletically gifted student.