No, the issue is not really with the allergies themselves, it’s the fact that people with allergies were specifically excluded from the trials at the screening phase.
As the saying goes, the devil is in the details, and one of the key details I most want to see is what other groups they might have screened out, and if that is reasonable or a blatant attempt to inflate their efficacy numbers.
I'm not so sure about the "fact" that people with allergies have been intentionally excluded. I am attaching the peer-reviewed Ptfizer's clinical trial data, which was published in the New England Journal of Medicine about a week ago. This is one of the most respected medical journals in the world.
As you can see, they tested a total of 43,548 participants and went through complete randomization. They even included many subjects (21%) with serious co-existing conditions, including HIV and hepatitis B/C infections. They didn't mention anything about people with common allergies. However, since about 30% of the general public has some degrees of allergies and they didn't specifically separate out these people, a significant portion of their subjects must have allergies. In their Figure 1, they listed that they screened an initial 44,820 subjects and eliminated 1272 (2% of their initial total) in the end for various reasons. As I mentioned above, ~30% of the general public has allergies. So these 1272 subjects cannot be those with allergies. So we have no evidence that they intentionally excluded allergies.
As you can see from their Figure 2, a significant portion of their test subjects suffered some degree of adverse effects, including some severe ones. They listed some of the common adverse reactions in the legend of Figure 2. Many of these adverse reactions are similar to allergic reactions. Please keep in mind that these side effects are common among all vaccines. So do expect to experience some of these when you get the shot too. However, if you compare the statistics of those actually getting the vaccine with those getting the placebo, you can see that the difference is not that big. Meaning that even people getting a placebo shot experienced significant adverse effects, even including some severe one (although not as much as those getting the actual vaccine). This suggests the vaccine itself is slightly more "dangerous" than the placebo. And no matter what you inject into them, some of them will react badly.
At the end of their report, they mention that they have separate studies focusing on younger kids < 16 and pregnant women. These studies are ongoing.
Again serious adverse effects with vaccines are expected. This is the same with every kind of vaccines, no matter which country designs and develops them. When the reports of Chinese vaccines come out, we will see the same trend. Nothing magical about Chinese or Western vaccines. They are the same. They have been rushed the same way. No need to discriminate them because of their origin. The Western media are criticizing the Chinese vaccines for the same reasons (lack of thorough testing, etc), and the Chinese are criticizing the western vaccines for the exact same thing. But if you look at these vaccines side-by-side, they are doing the exact same things, efficacy and side effects. If you want to respect science, let science take care of things.