Should "ate" and "eight" be pronounced exactly alike?

Is pronouncing "ate" and "eight" differently wrong? When I say "ate" it sounds like "ate" itself and when I say "eight" it sounds like "ey-ht" is that a wrong pronunciation? I understand pronunciation may differ from one person to another depending on the accent spoken by the person. But one of my friends told me that ate and eight must be pronounced exactly alike and if you're pronouncing them differently you are pronouncing one of the two words wrong.

Not necessarily. In BrE, ate is sometimes pronounced /et/, and the Cambridge Dictionary gives this pronunciation. Even if ate is pronounced like eight, there may well be subtle differences. In AmE, ate and eight appear to be pronounced the same. However, if you are learning English, I would recommend that you pronounce them both the same (/eɪt/).

Cambridge Dictionary: ate

Cambridge Dictionary: eight

There are two different possible questions implied here. One is for language learners, and one is for linguistics.

The answer, for the language learner (and native speakers) of General American English and British English (RP or Received Pronunciation) is that 'eight' and 'ate' are entirely identical.

The linguistic nuanced answer is there might very well be some subtle distinctions between the two based on the usual place in a sentence (one is a number and kind of adjective, the other a past tense verb). Or there might very well be dialects or varieties or sub populations that distinguish the two. There are many distinct dialects in the UK and US (many fewer in the US). Some of them say /et/ for 'ate', and most dictionaries specify it as a mainstream alternative to /eyt/ (common enough that it is considered socially 'unmarked'

But spelling is misleading in English. For almost all contexts, these two are identical.

Ate, ait and eight are all homophones. Dictionary.com defines a homophone as: Phonetics. a word pronounced the same as another but differing in meaning, whether spelled the same way or not, as heir and air.

This ultimately leads us to the result that your friend is right.