It's hard to believe that a woman her age could accomplish so much.

Question

would this be better saying

It's hard to believe that she accomplished so much.

or would this still be racist

From the data you give, it is impossible to tell what her race is, so how could it be racist?

If the race is known, you can give specific reasons why it is "hard to believe" to reduce the possibility of being accused of being racist. This might include lack of education, previous lack of accomplishment under similar situations, lack of social support or some other reason(s). This could also reduce the chances of seeming to be sexist.

I hope this helps. Thanks for asking.

so i am assuming the first sentence is correct i should not change it because there race and age was not told specific make this sentence nonracist and nonagist.

IThe trip was filled with goldenagers.
is this correct when stated as goldenager

No it should read "The trip was filled with senior citizens.

Actually it should read:
"The trip was filled with older people."

no it is not

<<It’s hard to believe that a woman her age could accomplish so much.>>

I don't see agism or racism in this, however, I do see sexism. Would it be easier to believe that a man at this age could accomplish so much?

The age...could be 24 years...

I would suggest this...
It's hard to believe that a person of that age could accomplish so much.

The only thing I can add Bob, is if there is a specific person being talked about I don't think it would be considered agist. For example, if she's talking about how her active 90 yr old granma does by comparison with her women friends, where's the harm done?
Context matters here I think.