Is it a mistake to play positional chess (e.g., d4) as a tactical player?

And vice versa: Playing tactical chess (e.g., e4 in many cases) as a positional player.

This is based on an untrue generalization. Tactical and positional chess are seamlessly interwoven in nearly every game that doesn't involve trivial blunders, and players should play according to the needs of any given position. 1.d4 can lead to wild tactical games: the games of Levon Aronian bear this point out. 1.e4 can lead to slow, more positionally oriented games: the games of Anatoly Karpov, especially in the closed Spanish, bear this point out. To answer your question, no, it is not a mistake to play 1.d4 as a "tactical player" (whatever that means), because it may be the case that the position that arises after the opening is over is in fact tactical, or if it is positional, then the player would do well to accomodate the needs of the position.

Yea like pointed out above d4 has lots of tactical lines. Semi slav triangle, botvinnik, anti moscow, kings indian bayonet, staunton gambit, etc.

And if you don't want to play c4 there is stuff like the Blackmar Diemar gambit. Its playable below 2200.

You need to learn how to play the position.

Just because you play e4 doesnt mean youre "tactical"  Just like playing d4 doesnt mean your "positional"

Get past the labels if you want to improve.

the easy answer is "No"...

how do they always put it?  Tactics appear from positionally superior positions.

Keep studying positional chess.