In 1944, it would not be a problem as much as it is now ("pogroms", seriously?). The main slant in politics in the middle east was whether you were pro and anti-British (or pro and anti-French where applicable). And this tended to (except in Palestine) cut across ethnic and religious line. The rich tended to be collaborators with the local colonial powers. It was the working and lower middle (and the tiny professional) classes which were anti- British.
The term "pogrom" is widely accepted as appropriate when referring to the anti-Jewish violence throughout the Middle East accompanying and immediately after the Israeli Independence War (or the 1947 Arab-Israeli War, if you prefer).
At any rate, you're right that it's irrelevant; the comment was mostly about the anachronism of an anti-Zionist Jew in Egypt.
So Nasser, who was fervently anti-British and while surprisingly devout for a committed socialist, would in 1944 see no problem in marrying a Jewish lady.
Absolutely, though I do suspect that there would be pressure on her to convert - from both sides, frankly; the relatively conservative Egyptian Jewish community would probably disapprove of the marriage very strongly.
How it may effect him post 1948, is harder to say. If he remains one of the leaders of Arab nationalism, then it might influence it in another was. Arab nationalism because of 1948 tended to be anti Jewish (this was not a religious thing, some of the most anti-Israel politicians were Christians). If he is married to a Jewess, then he might influence it away from that, appealing to the "Arab" part of the Arab Jewish identity. Israel was and to a large extent remain a very racist society, ( from what I have read they are less so) and E European Jews tended to look down upon Middle Eastern ones, and if Arab nationalism is not so hostile, then this might play a role in politics.
First of all, I'd like point out that "Jewess" is mostly considered to be Orientalist at best and openly derogatory at worst; compare Musselman.
Second of all, trying to incorporate Jewish Arabs into Arab nationalism is tricky. It's true that early Arab nationalism was not a purely Muslim endeavor and, in fact, it became openly anti-religious as it gained socialist traits. That said, looking at the facts, there was always a strong Muslim (and, specifically, Sunni) streak to it, especially since socio-economics meant that Christians throughout the Mideast tended to side with European colonizers over their Muslim majority countrymen.
Egypt was actually fairly good to their Jews, even after 1948 (though it's a very common mistake to overly romanticize pre-Israel Muslim/Jewish relations in the Arab world, which were hardly excellent. Even outside Palestine, including in Cairo and Alexandria, the early 20th century was marked by multiple outbreaks of violence against Jews in the Arab world), though a series of events (the Lavon affair, the Suez War) led to increasing pressure on Egyptian Jews, and their eventual final expulsion after 1967. In Egypt, as in the rest of the Arab world and frankly a lot of Europe and even the US, the foundation of Israel was followed by Jews being suspected as a possible Fifth Column; obviously this was especially problematic in countries that were at war with Israel. And God knows the Lavon Affair didn't help in Egypt.
It's possible that a high-ranking officer might be able to try and mitigate this, but I'm skeptical that he would be able to; there's not much a single officer can do to stop popular violence, especially when the rest of the military doesn't really support him. Certainly, there's almost no chance of a concerted effort by nationalists across the Arab world to try and include Jews (just as the effort to include Christians was luke-warm at best).
In a different world, where Arab nationalism gets its start a few decades earlier, and manages somehow to put an emphasis on pluralism (which, frankly, didn't happen very well in early European nationalism either), then such a phenomenon is possible, but we're looking at PoDs that are way bigger than Nasser at that point. It's also worth noting that European nationalism mostly excluded
their Jews, who were much more assimilated than those in most of the Arab world.
Fair enough, although I was thinking she could take a more openly anti-Zionist stance once the Israel-Palestine conflict breaks out.
It's possible, but it probably wouldn't do much. I'm skeptical that people would accept her sincerity.