I believe you are referring to the Racial Laws of 1938, which were indeed enacted as part of a policy of approachment to Germany after sanctions had been imposed by the League of Nations following Italy's invasion of Ethiopia. While the Fascist Party itself wasn't openly anti-Semitic prior to that date - and Mussolini's attitude towards Jews was very much unclear and ambivalent - the more anti-Semitic strains of the Party had already been pushing for such a thing as far as 1933 and these laws (as well as the Manifesto of Race) were enacted with relatively little opposition.

Albeit not every Jew was equal - "aryanised Jews", that is to say someone who in Germany would have been considered a mischling - were allowed relative freedom even if in the end, they shared much of the same restrictions other Jews faced. What made some Jews more "Aryan" than others, you might ask? A sentence of a particular commission established by the Ministry of the Interior, here's what.

Below are the more obvious impositions these people had to face:

• Marriage and sexual relations between "aryans" and "non-aryans" were to be forbidden.

• "Aryan" shopkeepers were mandated to put a sticker in order to certify that theirs was truly "an Aryan shop", whatever that might have meant (you aren't expecting Fascist legislation to make any sense, are you OP?).

• "Non-aryans" (which in this context really is just another word for 'Jews') could not attend public schools but those reserved to them, while being barred from attending universities - same thing for the Jewish teachers.

• Jews were barred from joining the Party, the Army (war veterans were forced to retire) and the p.a.

• Jews could not work as domestic helpers in "aryan" families, and viceversa.

However, it should be pointed out that the enforcement of these laws was quite lax outside of Italy, with most colonies (Libya being a partial exception as it was more tightly controlled than East Africa) proving to be a difficult environment in which to intervene, also given the State's limited resources and byzantine legislation.

As far as the influence Nazi Germany exercised on Italy in matters of race, I would be inclined to say that it just provided an occasion to unleash those anti-Semitic sentiments that had been building up for some years in the higher cadres of the Fascist Party and some strata of the Italian society. So yes... many of us had been willing accomplices of the Nazi regime and co-operated with it, if that's what you wanted to ask.

Even though there wouldn't be any deportation of Jews until Italy's capitulation in 1943 - after which what was left of the regime was more than glad to openly aid the Nazis by sending Italian Jews/dissents/partisans to the camps.

[...] I have heard that there where some Jewish members of the Italian Fascist Party who had to leave the party because Germany pushed Nazi racial politics on Italy. Is this true?

Sure, there were many people such as Aldo Finzi (one-time undersecretary of the Interior as well as one of d'Annunzio's closest companions during the so-called "Regency of the Carnaro") who had to resign from the Party.

[...] And what other effects did German Nazism have on Italian Fascism?

There was a whole kind of Nazi imagery Mussolini fell in love with, such as the goose step, which he saw fit to import and impose to an Army he was despised in; and what's more important, he began to be convinced of Germany's military might and invincibility - something which would lead our country towards war and its ultimate ruin.