The letter articulates our crisis of free speech
The signatories are right: free speech is being shut down. They are also right to use their platform to make noise about it. There is a legitimate crisis and a growing "intolerant climate" amidst us.
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Harper’s letter seeks to protect “the lifeblood of a liberal society” through calls of maintaining “the free exchange of information and ideas”.  In fact, the outcry from the letter indicates the need to review and debate the value of free speech. There were more than 150 artists and writers who cosigned the letter. Of the many who signed, a handful had more extreme ideas or more controversial careers. Upon hearing of these dubious signers, the public quickly rendered the whole letter as such by association, pressuring other signers to apologize for their signatures. The fact that the entire argument posed in Harper's could be "canceled" by pointing out the pasts of a few individuals who signed indicates the very issue they were trying to point out. There is a myriad of evidence indicating rapid censorship, but most fascinating is the state of US Universities, institutions who should be safe havens of expression and free thought. The William F Buckley Jr. Program at Yale found that “Almost half (49%) of US college students [felt] “intimidated” by professors when sharing differing beliefs, 72% say their college or university should be doing more to promote diversity of opinions in the classroom and on campus, [and] almost One-Third (32%) misidentify [the] First Amendment". The signers of Harper’s Letter were not only airing their own grievances with the free speech crisis, but they were also speaking on behalf of up-and-coming minds and think tanks: college undergraduates. Colleges are where individuals explore intellectual curiosity and themselves. Yet, many students feel increasingly uncomfortable sharing their unique opinions and thoughts, countering the very purpose of higher education and further proving there has been an assault on free speech. This was rightfully pointed out in the Harper’s letter.
Association can certainly delegitimize an argument. For example, you would not accept a medical diagnosis from a Physics teacher but would from a doctor because the doctor is qualified to give a diagnosis. In the same way, the backgrounds and reputations of the signatories delegitimize the letter.