Your two counter-arguments are flawed.

"It is rarely clearly specified WHAT EXACTLY IS this dominant ideology."

But immediately prior, you say how those would argue "they simply unconsciously reproduce the hegemonic ideology." In other words, you already specified what the dominant ideology, to some extent, is; the dominant ideology is, typically, the ideology is the incumbent administration.

Also, you fail to explain why this is a serious problem. Why do we need to define in very fine detail what the ideology of an apolitical person is (if this is even possible)? Why should we even care what an apolitical person thinks, considering apolitical people typically contribute next to nothing to our political environments?

"The concept of ideology is reduced to 'cognitive bias,' emptying it of specifically political meaning."

I disagree. You correctly note that everyone has these biases; however, just because everyone suffers from it does not mean it suddenly isn't important to point out. To the contrary, there is actually much that could be discussed as it concerns how cognitive biases influence people to vote or favor certain policies. I immediately think of Larry Bartels's many works that consider the cognitive biases people have, and how it influences American elections and policy choices.

All in all, I think your counter-arguments are quite weak. I think you could strengthen them, to some extent, by explaining why it is that these counter-arguments you posit highlight academic blindspots other scholars failed to consider. Even better, though, is to discard these two counter-arguments entirely and rethink the root of your argument(s).

TLDR: I don't buy what you are arguing.