True and not true. By itself, reducing straw use has negligible effects. It's whether it would lead to a change in behaviour (better management of use of plastic) that's key, I think.
It's covered as one of the FAQ questions [1]
[A]re straws a big deal? Not really. It's estimated that if all straws around the world's coastlines were lost to the ocean, this would account for approximately 0.03 percent of ocean plastics. A global ban on their use could therefore achieve a maximum of a 0.03 percent reduction. Why have straws in particular received so much attention? Probably because: (a) for most people (not all — some people struggle to drink without one), straws are unnecessary; and (b) it's a quick and low-risk step for businesses to be seen to be taking active steps in addressing this issue.
Reducing plastic straw use is — for the most part — not a bad thing to do. It can reduce plastic use a little. If this is a first step towards large-scale commitments to tackling plastic consumption, then it's a useful contribution. But as the late David MacKay noted: “If we all do a little, we’ll only achieve a little”. We must do a lot; we must tackle the high-impact options that will make a difference at the global level.
[1] https://ourworldindata.org/faq-on-plastics#are-plastic-straw...