Can I take non cash donations made this year in 2019 if I took the standard deduction for 2018?

Yes, you can certainly deduct contributions made in 2019 on your 2019 tax return.  You cannot take a deduction on your 2019 tax return for contributions made in 2018.

The rule is the same whether the contribution is cash or noncash.

What if I did not make a non cash donation on my 2018 return.

Tax law does not go by when you took the deduction.  You take the deduction in the year in which the contribution was made

Yes, you can certainly deduct contributions made in 2019 on your 2019 tax return.  You cannot take a deduction on your 2019 tax return for contributions made in 2018.