Heavybrisker – Judging by your screen name you would probably say no even if it was filtered! Filtered internet has also been banned by those same Gedolim shelo letzoirech.
But the very fact that you post online, and from observations I have picked up from the content of your posts, it seems that you would be quite happy with filtered internet.
But remember, not everybody is like you. Many people come from much more openminded backgrounds, which for them it is very accepted – and not entering the debate about right/wrong, it would defintiely not be a turn off for the shidduch if both sides are holding at the same stage.