Wouldn't... the critics that canned it be experts in comedy?
The critics who are used to calculate the critics score on RT are
not experts in comedy. Many of them simply have large enough YouTube channels or write for websites. If you have a sufficiently large YouTube channel reviewing movies/shows they might select you (this was actually the case for the first "critic" who gave Sticks and Stones a fresh rating). These people are not trained in stand-up comedy and they are not even specific to comedy as they supply ratings for movies and TV shows as well. If you wanted to obtain expert opinions, you'd have to consult actual successful comedians. Of the ones I've heard speak on the topic (which I do not present as an extensive or all encompassing list) they have been very complimentary of Dave Chappelle and his Sticks and Stones special. I'm sure you can find others that may disagree.
The audience are most definitely not experts of comedy either. My point is that neither the critics or the audience are experts in comedy.
Seems odd to dismiss every "critic' review while also propping up the audience reviews as some kind of validation.
A fair query, so let me discuss the key objective difference. For that I will turn to my old friend math/statistics. Obviously, I'll use the numbers that are available to us today and acknowledge that they may shift or change over time as more reviews are put forth.
The most fundamental difference between the critics score and the audience score is the sample size of each.
Let's start with critics score of 35%, which is based on 17 total reviews. That means that out of 17 critics, 6 rated the special as "fresh" and 11 rated it as "rotten".
Let's contrast that with the audience score of 99%, which is based on 36,984 total reviews. That means that out of 36,984 reviews, 36,614 rated the special as "fresh" and 370 rated is as "rotten".
From a statistical standpoint the 36,614 positive vs. 370 negative audience score is far more significant than 6 positive vs. 11 negative critics reviews. In statistics, as the sample size increases, the reliability of the data (and the conclusions that can be drawn from it) also increases. For our little example here, what difference does it make when 11 critics gave the special a negative rating, when at the same time 36,984 audience members gave it a positive rating? To prove the point, let's combine the scores...
Total reviews = critic reviews + audience reviews = 17 + 36,984 = 37,001
Total fresh ratings = fresh critic ratings + fresh audience ratings = 6 + 36,614 = 36,620
So our total RT fresh rating = total fresh ratings / total reviews = 36,620 / 37,001 * 100% = 99%
As you can see, the critics' reviews are mathematically insignificant when combined with the significantly larger set of audience scores. The audience score is significantly more trustworthy because it is is based on 2176 times the number of reviews as compared to the critics' ratings. This is based objectively on math alone, and I have yet to invoke any discussions or rationales based on right or left wing politics (we'll get to that below).. Without any of the further points I will make below, this should answer your question as to why I can dismiss the critics and at the same time prop up the audience score.
Now we get to the political stuff, which is at the heart of the thread topic. The Hollywood critics have a very large and obvious left-leaning political stance. I will use RT data to make this point because it is readily available and it is an amalgamation of critical reviews from various sources (newspaper, website, YouTube).
Obviously it is very difficult to make inferences on the critics' political bias based on only the Dave Chappelle: Sticks & Stones special. However, I've been following this topic for quite some time and as it turns out, that on average when a movie/show/special falls in line with leftist/woke/sjw agenda it gets great (better than deserved) critics scores. Conversely when a movie/show/special opposes the leftist/woke/sjw agenda it receives relatively poor critical ratings (as in the case of the Chappelle Sticks and Stones special). The problem with the critics scores is that they are based less on the actual quality of the movie/show and more on its alignment with leftest ideology. The way we can tell is when we see a massive discrepancy between the critics' rating and the audience ratings. Remember that the audience, although individual politically biased, are made up of people from both sides of the political fence, so they largely even each other out.
Let's look at a few examples:

This is the most pertinent and direct comparison we can make to Chappelle's special as Gadsby's offering is
supposed to be a comedy special as well. Hannah Gadsby's comedy special is extremely woke and what do we see, a 100% critics fresh score. Of course, the her work is significantly less funny (or successful) than Chappelle, which clearly evidenced by the audience score of 25%.
Up next, the series Doctor Who decide to take a woke spin (and not because the lead character is now a female) in its 11th season:

Just look at that discrepancy between the critics and the audience.
Moving on, let's look at

Here the gap between the critics is and the audience is smaller but is still highly significant at a 24% differential. What makes this rather interesting, is that if you read many of the critics positive reviews (the RT website links to the full reviews), many of them are searching for a reason to give it a fresh rating. Many of their reviews are not that flattering of the movie in terms of story, pacing, performance etc, but they still give it a positive because it is in line with leftist ideologies.
Moving on...
Here we have woke Disney Star Wars. Once again, the critics praise it and the audience trashes it. Admittedly the discrepancy is not purely due to left vs right leanings (though that is a very large component) as Disney has incredible sway in the industry and critics hoping to retain press passes to events and early screenings need to play nice.
And one of my favorite examples:
This was the first example of Marvel going woke. Even all the goodwill that Marvel had built up through 20 prior MCU movies could not save this movie from the audience. Of course, since it hit the right leftist notes, it was quite well treated by the critics. This movie is a particularly interesting case though, because prior to its release Rotten Tomatoes changed the site's layout/functionality to protect it. Prior to the release of a movie, fans could vote if they were interested in seeing the film or not interested in seeing it. This was not a rating of how good the movie was (because that option only becomes available once the movie is released), only if the person wanted to see it or not. Of course Captain Marvel fell to abysmal levels (in the 20's or possibly even in the teens by the end). RT quickly took away the ability for people to be able to vote on not wanting to see it. This stands even to today, where the only option available is to click on "Want to see".
One more

Star Trek Discovery whose acronym fittingly is STD, is the worst received Star Trek series ever. Once again, the poor quality of the series doesn't seem to deter the critics because it fits in line with the woke narrative.
Overall,the critics are either grossly incompetent or they are motivated by something other than the quality of the film/show they are reviewing. Critics, on a whole, are becoming increasingly irrelevant. Their scores are disassociated with the actual quality of the media they are reviewing and the actual audiences' enjoyment of it. How many people actually choose to watch a movie (or not watch it) based on what the critics say? I'll take the audience rating over the critics rating any day.