A lot of psychological studies are so poorly designed you can ignore the results completely for other reasons and not worry too much about this effect.
The Hawthorne effect doesn't necessarily apply to all people, nor does it affect all behaviors.
For example- it's difficult to poll people on some contentious topics. If you ask people, "Are you racist?" they tend to answer that they are not.
This doesn't call into question most or all polls. It just needs to be taken into account when designing and interpreting polls and especially with certain topics. The same applies to psychological research.