Rand doesn't deny that emotions are part of rationality, she denies that they are tools of rationality. It is rational to try to make yourself experience positive emotions, but to say "I have a good feeling about this" is not a rational statement, it's an emotional statement. It isn't something that should interfere with cognition.
As for emotions affecting humans behavior, I think all mammals have emotions, so it's not easy for humans to discard them over a few generations of technological evolution. Emotions were useful in the ancestral environment, they are no longer as useful as they once were.
but to say "I have a good feeling about this" is not a rational statement, it's an emotional statement.
If your hunches have a bad track record, then you should learn to ignore them, but if they do work, then ignoring them is irrational.
Even if emotions are suboptimal tools in virtually all cases (which I find unlikely), that doesn't mean that ignoring them is a good idea. It's like how getting rid of overconfidence bias and risk aversion is good, but getting rid of overconfidence bias OR risk aversion is a terrible idea. Everything we've added since emotion was built around emotion. If emotion will give you an irrational bias, then you'll evolve a counter bias elsewhere.
Another month, another rationality quotes thread. The rules are: