what do the majority of the YU רבנים, hold regarding an umbrella opened before Shabbos, is it permitted to use it, where there is a עירוב?

Thank you for your question I cannot speak for YU רבנים. However, I am quite sure that the honorable YU Rabbanim, would rule that it is forbidden to use an umbrella on Shabbos. This is the position taken by virtually all modern day poskim in the Jewish world today, without disagreement. Even if a few may not consider an umbrella to be in the category of an 'ohel' (meaning, use of a tent on Shabbos, which is strictly forbidden), it's use is still forbidden. Am Yisrael has accepted the minhag and psak of not using an umbrella because: a. someone may think that the user opened it up on Shabbos or b. because it is a ziluta deshabat and uvdin dechol (meaning that it is against the Shabbos atmosphere, a weekday activity if you will), and if someone violates it he is making a 'hole' (pirtza) in the gates of the halacha. Therefore, violating this activity would be considered worse than the violation of a regular sin. The Aruch Hashulchan went so far as to say that anyone using an umbrella on Shabbos has no 'fear of Heaven' (יראת שמים) because it is clearly forbidden. See Shemirat Shabbat K'hilchata, (24:15), Chazon Ovadia Shabbat, 5,page- 307) All the best