He considers that X is Y. vs He thinks that X is Y

Solution 1:

Acceptable is a loaded term.

Like @tchrist, I would not use sentence 1 in the form proposed. I would probably change it to "He finds blue cheese delicious." on the grounds of euphony.

But there is a spectrum of reactions from that sounds clumsy to that breaches several principles of grammar and syntax. Where you place "acceptable" within that span is obviously a very personal opinion. It is probably related to whether you consider "has to be" an acceptable replacement for "must be".

Solution 2:

This one gets a bit complicated. Consider

1. He considers blue cheese to be delicious. (618)

2. He thinks blue cheese to be delicious. (8)

3. He believes blue cheese to be delicious. (2130)

(OP's "blue cheese" was a bit too unusual to deliver a reasonable number of hits in Google Books, so I got the usage figures above by substituting "you").

As per the first link above, if you think something [to be true], that can often imply the thing is only (or even, axiomatically) true by virtue of your opinion. But if you believe it [to be true], your opinion has no effect on the truth of the thing itself.

So - if you think blue cheese is delicious, you're saying you like it. If you believe it's delicious, you're saying it's inherently delicious, so everyone else should like it too.

As the usage figures show, consider falls somewhere somewhere between think and believe in terms of how much your opinion thus expressed can affect the facts (mostly it can't).

Solution 3:

When I hear the the phrase "X considers Y," I tend to think it usually means something closer to "ponders." If it were phrased in a more passive voice, e.g. "X is considered Y by Z," it would sound more like the idea the other sentences are trying to get across.

Then again, "He considers blue cheese to be delicious" sounds fine to me, so it might just be that "considers that" is a bizarre-sounding way to format it.