The meaning of the underlined part

The meaning of the underlined part

The passage below is from The Library: A Fragile History by Andrew Pettegree.

After 1945, the speedy dissipation of the euphoria of victory, and the onset of Cold War anxieties, created a toxic environment for librarians. In 1950, Ruth Brown, the long-serving librarian of Bartlesville, Oklahoma, was dismissed, ostensibly for harbouring subversive material in her collection, in reality because she made no secret of her sympathy for the local African-American community. The ALA made little attempt to save her; apparently the matter fell between the jurisdiction of two of its committees, the Intellectual Freedom Committee and the Board on Personnel

Administration. Most of the ALA’s energies were at this point directed to fending off the implications of President Truman’s introduction of a loyalty oath for those in public service. With evidence that senior officials had been involved in trading nuclear secrets to Russia, news that the Soviets had the atom bomb and the outbreak of the Korean War, most citizens saw no problem in asking public figures

to give assurance of their loyalty to American values.9 When the Los Angeles county librarian was slow to sign the pledge, one library commissioner wondered aloud whether ‘our librarian … is free of those liberal thoughts that we don’t like in the head of our library’.

I have too many questions for the last sentence.

One Los Angeles county librarian was reluctant to sign the loyalty oath.

So one library commissioner wondered aloud whether ‘our librarian … is free of those liberal thoughts that we don’t like in the head of our library’.

First, meaning of ‘be free of’. Can I say it’s meaning is ‘be without’? (Am I right?)

Second, meaning of ‘liberal thoughts’. Here it seems to imply ‘the attitude of being slow to sign the pledge’. (Am I right?)

By the way what does ‘liberal thoughts’ mean in this context? (I think it is not an easy term to define and seems to have too many implicit meanings but to ask is all I can do right now.)

Third, does ‘the head of our library’ refer to ‘our librarian’? (Am I right?)

Forth, ‘we’ in the quotation seems to imply library commissioners including one wondering aloud. (Am I right?)

Last, the whole meaning of the underlined part is still a mystery to me.

My guess is that one library commissioner deplores his librarian had ‘liberal thoughts’ that library commissioners don’t like to have in his librarian. And he thinks ‘liberal thoughts’ is the reason of reluctance in signing the pledge. (Am I right?)

If I am right, the sentence is a catastrophe of logic. In that case ‘is free of’ doesn’t make sense to me. To make it sensible I think ‘is free of’ should be replaced with ‘is committed to’. (Am I right?)

(Last of last, meaning of ‘wonder aloud’. I googled out but cannot find out what it means. Only ‘think aloud’ in Collins Dictionary. It suggests it’s meaning is to express your thoughts as they occur to you, rather than thinking first and then speaking.

Does this can be applied to ‘wonder aloud’? If not, what does it really mean?

Actually I made my logic above with omitting this ‘aloud’ all together. Was that Okay?)

Thanks in advance. Thanks for taking all the trouble to read and even reply this labyrinthine question.