Would teaching that Asimov made those predictions be too religious in your view?

No, that is a fact that can be confirmed.

it matter if he had a bunch of people who took those predictions very seriously?

How are they taking it seriously? Are they sitting around designing rockets without having studied how to do so and without the ability to implement those designs? Are they fervently believing the predictions but not attempting to do things that are likely to help them come true? How much of their world view is affected by these predictions?

Not having specifics I am inclined to say most likely no.

if they thought that people should be educated about them?

I am a biased judge on this point. I am in favor of space travel. I know Asimov was as well. I think that Asimov was in a position to know something about space travel so therefore I am in favor of educating people about whatever he said (unless he said something completely crazy).

Is that too religious?

It would depend on the context.

If you tried on this sort of basis to argue that discussing uploading and strong AI in public schools was unconstitutional, you'd probably be laughed out of court.

Strong AI would get me laughed out of court by itself (probably). Uploading however could be made into a decent case.

Even stronger then someone that did not believe in the specifics of transhumanism would be someone that did believe in transhumanism attempting to gain the status of a religion. That would in my opinion get through the courts without any difficulties.