Fetching details from the dictionary...

to be obsessive (about); to be overly concerned (with); to fuss (over); to worry too much (about); to be picky (about); to be hung up (on); to stick to
to be particular (about); to pay special attention (to); to be fastidious (about); to insist (on); to be uncompromising
「拘る」 has another reading with different meanings.
細かいことに拘りすぎる。
I get too hung up on minor details.
彼は細かいことに拘る性格で有名でした。
He is particular about materials.
素材の産地に拘った料理が評判を呼んでいる。
The insistence on ingredient origins has earned the restaurant a fine reputation.