Psychologists have a concept known as "self-complexity" (wiki it). Basically, it's our view of ourselves, in terms of the many attributes, relationships, skills, deficiencies, etc. we possess. Someone who thinks of themselves in broad terms, filling many roles and with many aspects, is said to have a high self-complexity. Someone who thinks of themselves in terms of only a single aspect has low self-complexity. Think of "I'm a world-class kernel C hacker" vs. "I'm an awesome C programmer" vs. "I'm a good programmer" vs. "I'm a decent human being".
By itself, self-complexity is neither good nor bad, but it does have consequences. High self-complexity buffers you against negative events or negative appraisals of those aspects you identify with. Someone who's devoted their life to low-level kernel hacking is going to take it more personally when you say C is obsolete and only a fool would be involved in OS design in 2013. Someone who also sees themselves as a husband and a father and a good friend and a church leader and not all that bad at Javascript web programming either is probably going to let it roll off them; they may think you're wrong, but they'll just shrug and say "Whatever; you're entitled to your opinion" and not bother to argue the point.
So no, it's not bad for new activities to become part of your identity. It can be bad for them to become your whole identity, because it leaves you really vulnerable to outside attacks on your self-conception.
(On a side note, it seems to me that a lot of the Silicon Valley startup mythology is focused on encouraging low self-complexity and an obsessive focus on external success. Now that I re-read some of PG's early essays, several of them seem actively harmful to one's mental health. The YC application used to ask you "How are you an 'animal'?", in reference to an early essay where he suggested that successful startup founders often act like caged animals - as if denying your humanity is "success".)