Accelerationism is bullshit all around. Here, I will focus specifically on the left-wing variants of the ideology specifically to be more constructive, as any critique I could give about right-wing accelerationism would just be a critique of right-wing politics in general, and hopefully you've already heard enough of that to understand why right-wing politics is bad.
The central thesis of left-wing variants of accelerationism is that, if capitalism is left to its own devices, it will eventually destroy itself. Regardless of what kind of leftist (or post-leftist) economy you expect to emerge from the rubble, regardless of whether you expect capitalism to collapse in on itself violently or you expect it to simply achieve post-scarcity at some point in the far future, this reeks of bullshit to me.
My main critique of this line of reasoning is that its deterministic standpoint is foolhardy. What if capitalism never destroys itself? I can also assure you of this: proponents of capitalism have noticed that it is probably running itself into the ground. These people are not standing idly by as their beloved economy destroys itself; rather, they are actively working to find a way to save it. We cannot discount the efforts of these people in our fight against capitalism. We must take action against the economic system under which we live; we cannot just sit back and hope that it destroys itself, especially when capitalists will likely try to intervene to save it.
Another valuable critique of left-accelerationism lies in recognizing that it values the future over the present moment. Call me selfish or egoistic, but I want my life to be pleasant. I also want the lives of the people in my community today to be pleasant. Capitalism makes our lives unpleasant, so I want it to be dismantled during our lifetimes... there is no time to be waiting around for it to end on its own, especially if that time may not come until after we are gone.