- I have friends from all walks of life who/that/whom I consider my best friends.
In a sentence like yours, the usage of all three relative words ("who", "that", whom") are acceptable in today's standard English.
BUT, if you are taking a class, either as a native English speaker or as an EFL/ESL speaker, then you'll have to give the version that your teacher expects.
That said: Here's some grammar rationales.
First, let's parse the sentence a bit. The nominal headed by the noun "friends" is modified by the relative clause "who/that/whom I consider my best friends",
- I have friends(i) [from all walks of life] [who/that/whom(i) I consider ____(i) my best friends].
Notice the gap ("____(i)") in the relative clause. That gap could sorta be filled by the word "them" (in meaning only, though, not physically), and so, that gap has the function of object in that relative clause. And there is a link from that gap to the relative word "who/that/whom", and a link from that relative word to the noun "friends". They are all linked together.
Now, in a traditional grammar perspective, the expected "correct" answer might be the one expecting the relative word "whom", which is in accusative case. Teachers often want that because a pronoun that functions as an object is usually expected to be in accusative case.
But in practice, using "whom" in your example will make the sentence sound rather stilted. That is, a rather formal style.
Because the relative word is fronted (in front of the relative clause), we native English speakers will very often use the relative word "who" here instead of "whom". The relative word "who" is in nominative case, which is usually the case of pronouns that function as subject in a clause. Since the corresponding gap is not functioning as subject (rather, it is functioning as object), traditional grammars tend to frown on this type of usage.
But in practice, we native English speakers tend to freely use "who" (over "whom) -- except for the most formal styles.
Now as to the use of the relative word "that": we native English speakers also tend to freely use "that" (instead of "who" or "whom") -- except for the relatively more formal styles.
Some modern grammars (such as the 2002 CGEL) would consider the relative word "that" in your example sentence to be a marker of subordination, not a pronoun. And so, that eliminates entirely the old bogus argument put forth by pedants that the pronoun "that" shouldn't be used to refer to people -- and by the way, the pedants were wrong on that point too.
You can get some helpful info, somewhat, from regular dictionaries, in their usage notes on the entry of "that". But some dictionaries also have bad info.
You can get much better usage info on this topic by using a usage dictionary, such as Merriam-Webster's Dictionary of English Usage, in their entry on "that". Their info is readable and easy to digest.
If you're in an argument, er, disagreement, with your teacher on this, then you can get some grammatical support from the 2002 reference grammar by Huddleston and Pullum et al., The Cambridge Grammar of the English Language (CGEL).