I don't think anyone is stating that anti-Semitism is a stated core principle of communism, but it might be true that there is a strong positive correlation between people who are communist and people who are anti-Semitic. There is certainly a strong positive correlation between people who self-describe as communist and people who are anti-Israel.
The question then becomes, is there a strong correlation between people who are anti-Israel and people who are anti-semitic? I would agree that on the face of it, there is. However, I think the word "anti-Israel", as used here, is far too blunt to be of any use.
A simple test would be to see if these same self-described communists are against Jews in other contexts than in that of Israel and its external and internal politics. Do these self-described communists inconvenience, malign, attack, or protest against Jews in contexts where the politics of Israel are not relevant? As my claim (that they don't) would essentially be trying to prove a negative (self-described communists never do that), I assume it would be very hard for me to find hard evidence for my claim. However, I will say that
in my experience (for whatever that is worth), I have never found this to be the case (I assume we are talking about present-day people here, though would be willing to expand, if necessary). I will add as evidence, too, my previous statement that anti-nazi protests and marches typically are organised by the left (which of course includes other groups than communists), and that people on the left, including those who self-identify as communists, are the predominating participants.
I would therefore argue that being anti-Israel does not necessarily imply that the same person or group of people is anti-semite. This may very well be the case (I assume most nazis are both, for instance), but it cannot be taken for granted without a thorough analysis.
There is also the matter or Palestine. Are these self-identified communists anti-Israel regardless of its politics, or are they pro-Palestine? Of course it is possible, or even likely, to be both, but is it necessary? I would like to think that it isn't, as I do self-identify as pro-Palestine, but also as pro-Israel. However, this can also be tested easily. Ask a number of self-identified communists whether or not they would be anti-Israel if things were different. If there was peace in the Middle East, and both the Israeli and the Palestinians had a solution everyone was satisfied with, would these self-identified communists still be anti-Israel? As you are no doubt aware, the left complains very loudly when they believe Israel does something bad to the Palestinians, but only rarely cheer when they do something good. I would certainly like to interpret this as the left being content with the way things are, as long as the Palestinians and Israeli co-exist peacefully, but whenever the former is mistreated by the latter, they protest. I would like to interpret this as them being mainly pro-Palestine, rather than explicitly anti-Israel, but I have little confidence in that my interpretation is correct. If it was, why would they not cheer as loudly when Israel does something good as they boo when it does something bad? Of course, uneven media coverage may be a factor as well.
These self-identified communists are often anti-Israel because they believe that the state of Israel unjustly occupies territory it has no right to, and treat the non-Jewish population in these (and other) areas unfairly. This may or may not be the case; that is irrelevant here. What is relevant, however, is whether or not these self-identified communists similarly protest other cases where the perceived facts are similar or identical. Again, I draw mainly from my experience and from my friends on the left (many of whom self-identify as communists), and conclude that this is the case. Moroccan occupation of Western Sahara is protested against, as was the American occupation of Afghanistan and Iraq, and as is the continued American occupation of the Native American lands. Granted, apart from the middle ones, these protests are not as vehement, but I believe that has a lot to do with media exposure and that no one really seems to be arguing
for a continued occupation of Western Sahara, not outside Morocco, at least. The also protest against perceived oppression of a people by that people's own government, such as Iran.
I would therefore argue, based on my experience, that for several reasons, the term "anti-Israel" is too blunt to be equated, even implicitly, with anti-semite. Self-identified communists, in my experience, do not treat Jews or Israeli badly in other contexts, are typically pro-Palestine first and anti-Israel second, and do protest other cases which are similar in structure, but in which Jews play little, if any, part.
To use your analogy, there is nothing in veganism that has anything to do with your choice of route when you use your bicycle, but there might be a strong positive correlation between people who are vegans and people who choose a bicycle as a primary mode of transportation. Even though bike riding has nothing to do with veganism, it's entirely possible that a common group of values makes it so people who choose one are more likely to also choose the other.
And then these values perceived as common between the two groups would need to be analysed. Veganism is often, but not always, tied to environmentalism and animal rights. The vegan typically does not eat meat for a reason, typically because of perceived cruelty to the animals or for environmental reasons. This is in line with the choice of transportation. If the vegan is vegan at least partly for environmental reasons, it makes sense that these environmentalist principles would be likely to colour other parts of her life as well. Going by bike instead of car could be one aspect of that. I therefore believe it is likely that there is a true correlation here.
In the case above, I believe this is not the case. Yes, I agree that there is a correlation between being left and being anti-Israel, but I dispute the implication that there is a correlation between being left and being an anti-semite. People who self-identify as communists typically have a strong sense of equality, and are vehemently anti-racist, while nazis and racist typically place a low value on general equality (although equality within the group may be honoured) and are (often openly) racist. This aspect would speak against self-identified communists sharing a common set of values with groups that we know are anti-semites, such as nazis.
ETA:
I notice now, upon rereading, that I started switching from "self-described" to "self-identified" in the middle of the post. This was unintentional, but I do not care enough to edit it.