The only comment I have at this point is that the survey report doesn't help me to know what to expect if I were to visit a large number of American workplaces.

The terms are too vague, and the methodology too opaque.

What is "the political climate"? How are people supposed to measure it? Do people in each of the 2,000 workplaces that supplied respondents understand the same thing of this term, or something different?

What does "liberal" mean? Economically liberal? Socially liberal? Sexually liberal? Intellectually liberal? Measured how?

Same for "conservative". Even if the categories are self-selected, unless those terms are defined, how do we know what they mean? Is someone who believes the marginal rate of tax should be lower for wage income than for investment income and sex should only occur for procreation within a marriage whilst one participant is blindfolded and opiated, conservative, or liberal, and how staunchly so?

For this question: "Are you worried about losing your job or missing out on job opportunities if your political opinions became known?" a higher number of "Conservative" respondents indicated worry than "Very conservative" respondents. What are we to make of that? Could it have something to do with whether conservative respondents are employed in conservative workplaces or liberal workplaces? The data doesn't give us any insight.

What does the survey methodology tell us?

"The Cato Institute Summer 2020 National Survey was
conducted by the Cato Institute in collaboration with YouGov
who fielded the survey. YouGov interviewed 2,108 American
adults from July 1-6, 2020 who were then matched into a
nationally representative sample of 2,000 Americans aged 18 and
older. The margin of error is +/- 2.36 percentage points. This
does not include other sources of non-sampling error, such as
selection bias in panel participation or response to a particular
survey. "

Without any insight into the selection method, or the selection bias, the survey could mean anything. Or nothing with respect to the actual America that comprises 350 million people. But consider the opening claim of the article text:

"A new Cato Institute/ YouGov national survey of 2,000 Americans finds that 62% of Americans say the political climate these days prevents them from saying things they believe because others might find them offensive. This is up from 2017 when 58% agreed with this statement."

The survey did not find what "62% of Americans believe". It only found what 62% of 2,000 survey respondents answered in response to particular questions. There is a difference. We just have no way of knowing what that difference is.

The reported change between 2017 and 2020, of 4 percentage points, is less than the cumulative margin of error of +/- 2.36 percentage points each for the two polls.

So what is the new survey telling us? Are Americans more sensitive about offending other people? If so, is that a good thing or a bad thing? Or are they more wary about exercising their constitutionally protected right to free speech because of self interest? If so, is that a good thing or a bad thing?

I really don't know. I'd have to spend a good deal of time talking with a good number of Americans in a diverse number of locations and employment situations to even begin to develop an understanding.