To be clear the FSF's definition of free software is:
- The freedom to run the program, for any purpose (freedom 0).
- The freedom to study how the program works, and change it so it does your computing as you wish (freedom 1). Access to the source code is a precondition for this.
- The freedom to redistribute copies so you can help your neighbor (freedom 2).
- The freedom to distribute copies of your modified versions to others (freedom 3). By doing this you can give the whole community a chance to benefit from your changes. Access to the source code is a precondition for this.
It is also reasonable that some users would want to base their computing on all free software. There are good practical reasons for this. The one that is usually quoted is that you can fix bugs - but my guess is that this rarely happens in practice. The real reason is that using free software gives you a sort of assurance that the software will be available in the future and won't stop working because of a licence server closing it down.
If this is the case then why not worry about non-free software used on the server to deliver the webpage? It seems strange to focus on non-free software on the user's personal computer in this day and age of connected computing. The personal computer is no longer an island and to ignore the server in the moral equation is just inconsistent.
So we have to conclude that the FSF has gone a step too far and seems to be out of touch with the technology - or has just revealed itself to be a religion rather than a reasoning force for good.