iOS simulator is a handy tool available for every OS X user but you may encounter This Connection Is Not Private or other strange bugs when using it along some antivirus software.
If you have a problem with running your iOS App/WebApp inside simulator please check if you can establish any SSL connection. In my case it wasn't possible to connect to even https://apple.com.
After scratching my head a couple of times I finally found a solution which was changing Avast Security settings. Let's start from the beginning.
Open your Avast antivirus program and you should see something like this.
Under Tools tab you will find this popup.
Then you may try to click on Disable button next to Web Shield option and check if this resolves the issue.
If so reenable the Web Shield and proceed to the less radical solution :)
Click on the Settings link under the Disable button and you should see the following configuration.
The preffered solution would be adding Excluded servers with plus sign on the bottom of the excluded servers list. In the popup type in desired server address e.g. apple.com and select https in Service selection.
If you don't know the address or need more universal solution you may uncheck Scan secured connections checkbox but I think that this is less desirable solution.
This solution probably may be applied to other antiviruses which are scanning your SSL secured connections. Fell free to comment if you come across similar problem.
Official Apple forum - https://forums.developer.apple.com/thread/90510