I don't mind supporting websites by mining... but...
- It HAS to be the users choice to do so... so opt-in only !
- No mining allowed on mobile platforms (battery-life and all that...)...
- It HAS to be throttled so people's computers don't become slow/unresponsive...
- The owner of the website HAS to take responsibility for the code they use in case of malware / virusses being spread through their website...
As long as these conditions are met (particularly the last one) people shouldn't have a problem with it...