The two of them are close, but it doesn't interfere with work.
Tips
register
Slightly literary. Common phrases: 无碍大局 ("doesn't affect the overall situation"), 畅通无碍 ("flowing freely / unobstructed"), 圆融无碍 ("completely harmonious without obstruction," Buddhist register).
history
In Buddhism (especially Huayan school), 无碍 describes the perfectly unobstructed interpenetration of all phenomena - 事事无碍 ("phenomenon and phenomenon do not obstruct each other"). The everyday "no problem" usage descends from this metaphysical sense.
