Learn English – Either of those teams or either of the teams

You can use either of those phrases for this purpose, they are both grammatically correct and carry mostly the same meaning.

However, there is a subtle difference between them that might mean the first option is preferable.

Indeed, the second phrase,

Either of those teams.

could be understood as insinuating that there are more than 2 teams participating in the match since you apparently needed to specify that you were talking about "those" teams and presumably not the others. There is no such potential for misunderstanding with

Either of the teams.

here, the use of the definite article "the" emphasizes that the two teams denoted by "either" are in fact representative of all the teams. There are only two teams and the speaker is discussing them both.

While all this is true, I do want to repeat that the difference is subtle and that in practice it's unlikely anyone would actually be confused about the number of teams that are participating in the match (unless it's a game they've never heard of before), so effectively you can use either sentence, especially if conveyed verbally.

On a side note, the correct phrasing would be "You can't side with either of those/the teams". Without the "with" both sentences are wrong. Also, if you felt so inclined you could skip "the/those" and simply say "You can't side with either team." It's grammatically correct and actually the way most native speakers would probably phrase it.