WriteStreakJapanese

We can agree to disagree.

NHK's article about だ抜き discusses native speakers' use of だ before と where a clause includes more than one word. In such cases, people tend to add だ.

• [○]明日は晴れだと思う。　[?]明日は晴れと思う。

• [○]彼の名前は田中だと勘違いした。　[?]彼の名前は田中と勘違いした。

• [○]彼が実は無実だと認めてください。　[?]彼が実は無実と認めてください。

• [○]私は、彼女は英雄だと見なしている。　[?]私は、彼女は英雄と見なしている。

• [○]自分の意見は常に正解だと思い込む。　[?]自分の意見は常に正解と思い込む。

  (○: fine, ?: questionable/clumsy/unnatural/highly-colloquial/etc)

In these cases, ones without だ look more or less clumsy to me, because the part before と is essentially a sentence with a verb and a corresponding subject.

(quoted sentence with plain form ending) と (Your verb. i.e. 言う、思う、聞く、etc)

So really what comes before the end of the と particle in this case is the plain form. I think that several examples will help you out.

彼女は綺麗です。(She is pretty)

綺麗 is a な adjective. Using it at the end of a sentence, we get です, or in plain form だ instead of な。

彼女は綺麗だと思います。(I think that she is pretty.)

Taking the first example sentence, and putting it into plain form, we can add と思う。 Without any complications.

あのビルは大きいです。(That building is big.)

大きい is, of course, an い adjective. In the sentence I ended it with です (to be polite), but です in this case is unnecessary. I could say あのビルは大きい and still have it mean the same thing. Plain form with い adjectives actually end with the adjective, which in this case is 大きい。

あのビルは大きいと思います。 (I think that building is big.)

I'll give you a few more examples without commentary, to hopefully solidify the point.

あの人は大学生です。(That person is a college student)
あの人は大学生だと思います。(I think that person is a college student.)
彼は十キロ走っています。(He is running 10 kilometers.)
彼は十キロ走ってると思います。(I think that he is running 10 kilometers.)

Additionally:

A verb clause can be phrased by adding 「と」 to the end of the clause. For clauses that end in an plain noun or na-adjective, we must add 「だ」. A direct quote would use the Japanese version of double-quotes: 「」 but you can also paraphrase.

https://guidetojapanese.org/learn/complete/verb_phrase