Awareness is when you are conscious of something as it is. Acceptance is when you feel that you don’t need to put in an effort to change the situation. You can strive to be aware of as much as you can. Whether you accept the status quo, is a choice that you must make.
You may be aware that systemic racism exists, but you should not accept that this is the way that it has to be. On the other hand, you may be aware that your project may be delivering a mediocre change, but you might accept that this is the best you can (or want to) do with the current resources and skills.
A difficulty with the act of acceptance is that it is almost a passive response. Acceptance is simply the moment when you know that you are aware of the current state, and you decide that there is no more energy that you want to expend on a different future state. This is why acceptance of misinformation, prejudice, and anger can become prevalent and dangerous.
Be aware of how things are, and if you are going to accept the current state, make it an active acceptance, not acceptance, because you don’t care enough.