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Bolsonaro's anti-vaccine stance in the face of more than 180,000 covid-related deaths in Brazil may strike many observers as political suicide, but a lot suggests the president's gamble may not hurt him politically. 
First, remember that Bolsonaro must keep his loyal followers mobilized and society polarized. Deepening polarization is mandatory, no matter in which context. The anti-vaccination stance is just another reiteration of the same old pattern: the more polarizing, the better.
Supporting the anti-vaccine movement is particularly useful to fuel the battle between the globalist and arrogant elite vs. the common man. Even Bolsonaro voters who are neutral about the vaccine realize that elites often regard them like hillbillies stuck in the Middle Ages.
Second, the anti-vaccine strategy allows Bolsonaro to dominate the debate and keep the opposition stuck in a maddening circle of whether to call Bolsonaro "assassin", "genocidaire" or if he should be taken to The Hague. Bolsonaro supporters love the spectacle.
Third, the vaccine rollout will the frustratingly slow. Mistakes will be made. By not leading the effort, Bolsonaro can deflect all the political blame if anything goes wrong. He can sit back and retweet fake news, for ex about people who supposedly died after getting the vaccine
Bolsonaro's message is totally consistent with his denial of the threat the pandemic poses to public health - a strategy that, so far, has been politically successful. In a recent poll, only 8% of respondents thought Bolsonaro to be primarily responsible for the 180,000 deaths
Fourth, while Bolsonaro embraces an anti-vaccine rhetoric and speaks about supposed risks and dangers of the vaccine, his stance is carefully calibrated: he won't actively hinder its purchase & distribution, allowing more moderate supporters to dismiss this rhetoric as secondary.
