Native English speakers, please help me out

I got into an argument about wether it’s ok to say “I think yes” and “I think no” in English. Here’s my opponent’s comment:

(It's possible either way. Native speakers use both versions, understand each other perfectly, and so on. There's no definitive rule here. Yes, it would be a mistake when writing complex texts and official essays and in various exams, but in spoken language it doesn't matter. Even in the IELTS speaking section, both versions are accepted).

Is it really so? I usually hear people say “I think so/I don’t think so”, am I wrong?

Question

Native English speakers, please help me out

I got into an argument about wether it’s ok to say “I think yes” and “I think no” in English. Here’s my opponent’s comment:

(It's possible either way. Native speakers use both versions, understand each other perfectly, and so on. There's no definitive rule here. Yes, it would be a mistake when writing complex texts and official essays and in various exams, but in spoken language it doesn't matter. Even in the IELTS speaking section, both versions are accepted).

Is it really so? I usually hear people say “I think so/I don’t think so”, am I wrong?

Answer

As Abby Teaches English say inm a round-about way, yes it is fine, but not commonly used.
Is it ok? I think, yes. I know, yes.

Answer

“I think yes” and “I think no” are not wrong grammatically, but they are unnatural in normal conversation. Native speakers almost always say “I think so” or “I don’t think so.”
The only time “I think yes” or “I think no” sounds natural is when someone is choosing between the two words themselves, for example:
A: Should we go? Yes or no?
B: I think… yes.
Outside of that narrow situation, native speakers avoid those phrases.
So your instinct is correct. “I think so” and “I don’t think so” are the normal, natural choices in both speaking and writing. 
I can tell you, as a native speaker, if I hear someone say, "I think yes/no," that tells me they are not a native speaker.