I’m slightly exaggerating, but it would absolutely empower reactionary conspiracy theories and give them ammunition to draw disaffected poor whites into their echo chambers. There’s already a persistent conspiracy theory that the (((global elites))) are conspiring to stop white people from eating meat (to make them weaker and less masculine) and this would just empower them.
I fail to see how your counterproposal to outright ban meat would not lead to this same scenario (probably faster).
Also, you're ignoring the option to provide a divedend (monthly, if you like) to citizens from the tax revenue to offset increased meat prices. With the dividend, the poor would be largely unaffected, and mostly the result would be the middle class reducing their meat consumption from excessive to moderate.
Also also, you keep talking about how this scheme bans poor people from eating meat. But I have to say, this reminds me of the criticism that gas taxes hurt poor people since now they have to pay more for gas - ignoring the fact that many poor people simply don't drive cars, because they are too poor to afford them. And so a gas tax spent on improving transit ends up helping the poorest, because what people need is transportation, not cheap gas.
Also also also, if this sort of scheme were ever implemented, I highly doubt it would result in widespread food riots like you see in a developing nation when they are literally starving in the streets. Worst case, it would result in the people who implemented it being voted out of office and having the policy rolled back. And with a dividend program and a gradual pricing rollout, this would be even less likely.