There are things that are reasonable to ask of presumptive nominee for Secretary of Defense Hagel, and things that are not.
As to what is not really very important, those involve his remarks about the Ambassador and his "agressive" homosexuality, and the Israeli lobby, as opposed to policies involving Israel.
As to the former and why, read a little bit about the Ambassador in question, a very generous donor to the LBGT community, and a great guy it would seem like, but if one is honest, one can see Hagel's point in the world of 1998 on that issue, as to very assertive demonstrations of an identity not everyone then took so for granted now.
As to the Israel lobby remarks, it is a fact of life that there exists a lobby for Israel that is very powerful in the United States, if its many of its most vociferous exponents are fundamentalist Christians, not Jews, as to why the latter shouldn't freak out about Hagel being an anti-Semite. That is a slander that often creates anti-Semitism as much as any other effect.
Lots of people have wondered if those lobbying America allegedly for Israel might in fact not be doing Israel any good at times, as to encouraging assertions of maximal Israeli interests that might not be in Israel or America's interests, factually speaking, especially because it is often done by Christians with apocalyptic views, in which the very existence of Israel is supposed to bring on the end of times.
On the other hand, people who see Israel as the main problem are often at best grotesquely naive about the Arabs and Muslims.
As to policy disagrements here with respect to Israel, that is another story entirely, although the Hagel nomination, should that be the case, if it seems inevitable, would be a good time to honestly discuss those differences, unlike the laughable obsequiousness demonstrated when Netanyahu visited the House in 2011.
Surely even Bibi found that a bit much, at least upon reflection.
As to policy, Hagel is criticized for wishing to speak to Hamas, Hezbollah, and Iran.
Although many, if not all, observers view that as a pointless exercise, even harmful, it would be useful to allow Hagel to explain his theory of why that makes sense.
That is especially the case with Iran, because that decision cannot be evaded forever, because Iran's centrifuges are spinning, and Israel as a factual matter would seem unlikely to wait forever to have that reach its logical capability, like it or not.
There are many issues in the Defense Department that have been coming down the pikc for a while now beyond the Iranian question that need a vetting, things like choices of how to deal with budget austerity.
Having a calm discussion of those issues with whoever is to become Secretary of Defense, with Hagel as the presumptive nominee, is rather more important than it has been in a while, in which reasonable objections are the ones we should spend our time on, so that the American people can have at least some sense of what are the issues facing their physical security protected by the Defense Department.