Avos Chapter 2, Mishnah 3. Rabban Gamliel, the son of Rabbi Yehudah HaNasi - this is Gamliel the Third - continues and teaches the proper way to conduct oneself with the authorities:
"Hevu zehirin barashus" - be careful of the authorities and of the government.
"She'ein mekarvin lo la'adam ela l'tzorech atzman" - they draw a person close only when they have need of him.
"Nir'in k'ohavin bish'as hana'asan" - while they are benefiting from him, they appear as though they genuinely care about him.
"V'ein omdin lo la'adam bish'as dochko" - but they do not stand by a person in his time of distress.
The relationship to Shammai's mishnah:
This mishnah seems to stand in contrast to Shammai's words in mishnah 10 of the previous chapter: "Al tisvada larashus" - do not make yourself known to the authorities at all. Beyond the fact that Rabban Gamliel is sympathetic to, and recognizes, the reality of the need to deal with the government more than emerges from Shammai's words, the Bartenura (and many commentators along with him) explains that Rabban Gamliel is addressing the leaders of the community and the leaders of the Jewish people, who are under the protection and even under the control of the authorities - in this case, the Roman authorities.
The fundamental message is this: yes, communal leaders have no choice but to be known to the authorities and to maintain contact with them, since these are the political realities they must deal with. But they must not fool themselves into thinking that the authorities are their friends. They must navigate their dealings with them very carefully, because in the end the authorities want one of three things from them:
Tax payments.
To use them for their own purposes.
To obtain information and intelligence about the community.
And none of these is for the good of the community.
Historical background:
Rabban Gamliel the Third lived at the beginning of the third century C.E. This period was most likely the high point in relations between the Jews and the Romans, during the days of the Severan dynasty in Rome, and the situation of the Jews in the Land of Israel was relatively good - at least for a short while longer, before things would take a turn for the worse. Against this backdrop he warns: even if the situation is good right now, do not delude yourselves. The closeness stems from self interest alone, and the Jews must understand that they need to look after themselves and be realistic about how the authorities regard them.
Application in our own times:
The mishnah is indeed speaking about Jews living under a gentile government, but it may apply just as well to Jewish communities in the twenty first century living under an Israeli government. This is not an anti Zionist statement in the slightest; the point is that a government is a government, and Jewish values or the interests of the Jewish community are not necessarily at the top of its priorities, since other considerations guide it. Therefore, Jewish communities in the twenty first century do indeed need to work with the government, and ideally it would even be fitting for the government to align itself with the values of those communities - but they must not fall into the mindset that the government has the same values and the same interests as the individual Jewish communities within the State of Israel.