They have an almost legitimate concern about safety -- bikers are notoriously reckless on city streets, which is one of the reasons that it makes such good sense to restrict them to their own lanes.
But the main issue is the "scantily clad cyclists - especially sexy women" who ride through the neighborhood, and who distract the supposedly observant men from their supposedly lustless prayers, thoughts and business dealings.
We have two thoughts on this typically stupid New York story. First thought: Suck it up, guys. The truth is that we live in a world full of pretty women, and (most) men are hardwired by nature to find them distracting. As long as there are women, you will be tempted to lust; as long as there are women to whom you are not married, you will be tempted to adulterous lust. The true spiritual challenge which faces you is not to build a wall against temptation, but to resist it.
Second thought: It isn't the government's job to assist in your spiritual quest. It is the government's job to accommodate the diverse needs of a diverse city, which -- given NYC's overcrowded streets and paucity of bikeable paths -- most certainly includes the creation of more bike lanes.
(A tip of the biretta to Father G. Hussein Thomas, for drawing our attention to one more assaut on secular society).