Firstly in my original post I stated why I don't believe YouGov to be accurate. It isn't just me that has an issue with thier polling.
Secondly, It is well known that many people are swayed by peer pressure and/or what is perceived to be popular. Therefore if you can manipulate polling to show something is popular, then it can sway people that are more influenced by peer pressure/on the fence.
Often in advertising they will site a stat about customer satisfaction. In the small print it will state the sample size or the methodology and it is often hilariously unrepresentative. Obviously they are relying on people not reading the fine print and being statistically illiterate.
Politicians, governments and corporations have been using various tactics throughout the 20th and 21st century to sway public opinion, both home and abroad to their favour.
This issue has divisive for years and has historically had a huge amount of push back. You can see this in the surge of VPN downloads (which is a form of protest against these laws), the popularity of content covering this issue.