So what's kind of amusing about your framing of the question is that you are making it sound like the West didn't want to help the Soviet Union because of its ideological biases. But it's really the other way around: the ideological biases of the Soviet Union kept them from refusing any help from the West!

The Soviets did not make any announcement, even to their own people, about the Chernobyl accident as it happened. The reasons for this are complicated. They were partially in denial about it; it just seemed inconceivable to them, and it took them time to really acknowledge the gravity of the situation. They also were a reflexively secretive government; they saw this kind of thing as a sign of weakness, as potential evidence of a non-perfect system, and possibly as an indictment of their approach to running things. And it was also a system where the bearers of bad news were often punished for the bad news, so it took a long time for the various officials, technicians, scientists, and so on to really acknowledge how bad it was. So they not only didn't tell their own people (or even themselves) the whole story, they didn't tell the West at all.

It wasn't until two days after the accident that radiation was detected in a non-Soviet nation. A nuclear power plant in Sweden was equipped with radiation monitors which were triggered by a worker entering the plant. At first they worried that it was a problem with their reactor, but they quickly figured out that the radiation was outside of the plant, coming in with the wind. They did some calculations and realized it must be blowing in from the Soviet Union, and that if the radiation levels were that high as far away as Sweden, then something really terrible must have happened. The Swedes contacted the Soviets to ask what was up, and were told nothing had happened. However enough radiation was coming into Sweden, Denmark, Norway, and Finland that it was pretty clear that not only had something specifically gone wrong with a reactor (the isotopes were pretty "fresh") but that whatever the source of it was still releasing information (it was not a one-time leak or venting, but a continuous thing).

When the Western media broke the news of the radiation, the Soviets had still not said anything about it to their own people. The US attempted to broadcast information about it into the USSR on Voice of America, but the Soviets jammed the frequencies and denounced the reports as lies. Within the USSR, a big rally and parade that had been previously scheduled to take place went on in Kyiv, like nothing was happening, despite the area receiving much more radiation than people ought to be exposed to.

Finally, a day later, the Soviet news agency TASS read out the following statement over the radio: "An accident has taken place at the Chernobyl atomic electricity station. One of the atomic reactors has been damaged. Measures are being taken to eliminate the consequences of the accident. Assistance is being given to the victims. A government commission has been struck to investigate what happened."

Which is not much and certainly gives no indication of the scope and scale, much less the danger, of the accident. And no newspaper took up the report — it was just over the radio!

Anyway, at this time, the Reagan administration did offer assistance to the Soviets, via the senior Soviet diplomat in the US. It went nowhere; it is not clear that the diplomat even knew anything about the accident, much less had any ability to accept assistance. Reps for the US State Department then made some disparaging comments to the press about how Soviet secrecy was a real problem, and the Soviets, in turn, criticized the US for being critical of them. The US did not really expect the Soviets to accept help, to be sure; they knew how they were and how secretive they were about accidents and nuclear things, and they believed (incorrectly) that Chernobyl was part of the Soviet military program. (See this recent discussion about why they might have thought that.)

Several days later, as the full scope of the thing was becoming more apparent, there were some individual efforts by Americans to give some small amounts of help — medical supplies, even a doctor who went over to help treat patients — but the Soviets were not interested in accepting help on a large and official scale. They spent a lot of effort essentially reminding the world about Hiroshima and Three Mile Island as ways to deflect from their own problems.

So yeah, you are right that people in Europe and the US and elsewhere viewed this with alarm! But what is remarkable is that the Soviet attitude of suspicion and defensiveness meant that they really did not accept any assistance in almost any form. Much of this was from a reflexive secrecy and a way of doing business that had become extremely calcified. The way in which Chernobyl exposed these aspects of the Soviet state to its own people in a very vivid way is sometimes held up as one of the things that led to its collapse only a few years later, but that might be a stretch.

For a very good, popular discussion of the accident and especially the Soviet mindset during it, I cannot recommend Serhii Plokhy's Chernobyl: The History of a Nuclear Catastrophe (2018) enough. It's a great read and Plokhy is extremely interested in exactly why the Soviets reacted the way they did.