As the owner of your charting spreadsheets you control who else has edit access and who has viewing access.
Note that these important security settings apply to the whole spreadsheet. If you have charts that are a work-in-progress it is advisable to keep them in a separate non-public spreadsheet, and then copy them to your public spreadsheet.
Click the blue Share button top right.
Enter the email addresses (preferably Gmail) of specific people and grant them edit or view access
Click Advanced to access Link Sharing. Here you can make the spreadsheet Public on the Web , or viewable by Anyone who has the link. This is essentially the same as publishing the spreadsheet.
Be sure not to grant these anonymous people edit access.
You can now publish the shareable link either in its long form or after putting it through a url shortener.
On a desktop operating system this link will open the Google Sheets web interface in view-only mode and any updates will be pushed to the client so they will not have to refresh their browser to get updates.
On mobile devices the behaviour seems to depend on the browser and type of device. When using the Chrome browser on Android the link will automatically open the Google Sheets app in view-only mode. This is the preferred behavior as the app provides a superior user experience compared to a web browser.
An alternative method os to go File > Publish to the Web, where you can choose one of several display formats.
This method may be better for historical charts than for current charts that you want to update in real-time.