How did Hitler's commitment to the final solution hinder Germany's war effort?

Yes, but not likely to any significant degree.

The major impacts of the Final Solution were threefold:

(1) occupying approximately 1 division's worth of SS troops for garrison, guard, and other related activities

(2) redirection of rolling rail stock (i.e. freight trains) from carrying war material to carrying Jews to the extermination camps

(3) killing a rather large potential (slave) labor force, rather than make use of their skills in the war industries.

All three of these were very minor hindrances, and did not really influence the outcome of WW2 in any meaningful way.

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While not part of the Final Solution, the pre-war discrimination against Jews in Germany caused a large majority of the educated German Jewish population to emigrate elsewhere, primarily to the U.S. This was probably the biggest influence that Hitler's hatred of the Jews had on Germany's chances to win, as a major section of Germany's best scientific minds were lost to the Allied side.