Why might the romans in Judea especially have responded harshly toward anyone arousing strong feelings among the Jewish people?

Answer 1

The greatest crime in the Roman lexicon was that of rebellion. They were constantly concerned that rebellion might spread unrest throughout all of their colonies. Judea was centrally located and possessed a populace with religious motivation and with belief in Redemption.

Background:

Hyrcanus and Aristobulus, the two sons of the Jewish King Yannai (Johanan Hyrcanus, 1st century BCE), got the Romans involved in Judea when they asked them to settle a dispute. At first the Romans were cordial; and they actually became party to a military treaty with Judea (Talmud, Avodah Zara 8b). The Romans didn't interfere much in Jewish internal matters, because the main thing that they wanted was taxes and a quiet populace.
A couple of decades later, however, they unilaterally abrogated the treaty, and placed Roman governors over the land who afflicted the Jews with crushing taxation (Talmud, Yoma 9a).

In the first two centuries CE, things got worse, with the Romans destroying Jerusalem and the Second Temple after the Jewish Zealots attempted to revolt. The Romans sold hundreds of thousands of Jews into slavery (Josephus). From time to time they forbade the observance of the Torah-commands, and they killed several of the leading Sages, despite the fact that the Torah-leaders had advised against revolt (Talmud, Gittin 56a).

Later, Simeon Bar Kochba led a second revolt, in an ill-advised attempt to recreate the independent Judea. The Romans responded by destroying Betar.

See also:

Jewish history timeline

The Jews and the Romans