It's hard to make any kind of general judgments about partisan movements like the Polish resistance, because they tend to be diverse groups whose primary or sole commonality is that they are anti-regime. Some of the Polish resistance were conservatives, some were liberals, and some were communists — and of those, some were Soviet-aligned and some were avowedly not.

So the Home Army (the armed wing of the Polish government-in-exile) represented a broad church but essentially democratic-republican movement. The People's Army, meanwhile, was directly linked to the Polish Workers' Party and from there to the Soviet Union — and declined to merge into the Home Army when many other resistance forces did.

There were certainly many Polish Jews involved with the resistance, and there were wholly or predominantly Jewish partisan groups. The most famous of these are the Bielski partisans (on whom the film Defiance was based) but you also have the United Partisan Organisation in the Vilna ghetto and the Jewish Military Union/Jewish Combat Organisation, which played substantial roles in the Warsaw Uprising.

Here's some interesting home-grown research on Jewish partisans in Lublin, which also looks at the relationship between Jews and non-Jewish resistance fighters in that region — and which includes some remarks on antisemitism among those groups. And here and here are a couple of interesting essays reviewing the historiography around Jewish resistance.

As a general remark: you have to consider that antisemitism was a far more widespread phenomenon in early 20th century Europe than it is now, and was by no means limited to the Nazis. The history of antisemitism is a very long and very unhappy one, and one in which most European nations and societies have played a role.

To add onto k1990's excellent answer, it's important to keep three very vital contexts in mind when grappling with the nature of Polish antisemitism during the Second World War.

• The European context: antisemitism was neither a uniquely Polish nor German phenomenon and had a relatively wide acceptance within Europe. Furthermore, an important proviso is that antisemitism often came in different shades and types. Justifications for antisemitism could vary widely between states and range from a grudging toleration for Jews (Rudolf Virchow, a nineteenth century German Liberal supported assimilation because "The Jews are simply here. You cannot simply strike them dead.") to outright biological racism. Not surprisingly, there was a similiar variety of antisemitism within Polish political and popular opinion.

• The Interwar Polish context: Polish nationalism was born out a very unique situation that complicated the relationship of Polish nationalists to Jews. The core heartland of Versailles Poland were the former Prussian and Russian territories and both these imperial states were very hostile towards any expression of Polish nationalism. There were very stringent laws against the Polish language and both Orthodox Russia and Lutheran/Protestant Prussia discriminated against the Catholic religion and individual Catholics. These two markers of national identity (Polish language and Catholic) became very central to the now independent Poland's sense of national self. The Jewish retention of their own language (Yiddish) and faith placed them as outsiders within articulations of Polish national identity. There's a remarkable document that illustrates some of this: Zofia Kossak-Szczucka's 1942 pamphlet Protest. This was a very courageous document that was distributed in Warsaw in the aftermath of the liquidation of its ghetto. Kossak-Szczucka asserted that it was the Poles' duty as both good Poles and Catholics to resist the murder of the Jews and those who stand by:

Those who do not understand it and want to connect the proud and free future of Poland, with contentment of grief of fellowmen, is neither a Catholic nor a Pole.

Notice in Protest the notion that these were Polish citizens who happened to be Jews being murdered is absent; the Jews were human beings but not fellow Poles. Now Kossak-Szczucka was very heroic and not an antisemite in any sense of the word, but also held but as gingerkid1234 points out bellow, had very complex sentiments about Jews. Protest illustrates elements of the exclusionary tendencies of Polish nationalism.

• The Wartime context: Something that has a tendency to be overlooked when examining Polish antisemitism in World War II is the role of the Third Reich in enabling it. There were no disincentives against antisemitism within occupied Poland, in fact the Nazi authorities in the Poland explicitly punished any actions that helped Jews. This had the consequence of unmuzzling much of the latent antisemitism within Polish society. Furthermore, the Nazi occupation's restrictions on Poles encouraged and rewarded apathy among the Christian population towards the plight of the Jews. So some of the antisemitism within wartime Poland represented these greenhouse conditions.

Sources

Bankier, David, and Israel Gutman. Nazi Europe and the Final Solution. Jerusalem: Yad Vashem, 2009.

Snyder, Timothy. Bloodlands: Europe between Hitler and Stalin. New York: Basic Books, 2010.

Weeks, Theodore R. From Assimilation to Antisemitism: The "Jewish Question" in Poland, 1850-1914. DeKalb, Ill: Northern Illinois University Press, 2006.