'Keep your identity small' is a rationalist proverb coined by Paul Graham. It reminds us that identity is often an obstacle to objectivity. That is, while it is possible to have calm, collected, and entirely correct discussions on religion, politics, and which programming language is the best, we often fail at these things very badly. This is often because we start defending our personal beliefs and take disagreements as attacks against our identity.
One factor at play here is that things like religion and politics are free to enter; you might not feel that you personally have earned the right to have a strong opinion on the Copenhagen interpretation, the offside rule, or Pi vs tau, but you probably feel that you have an absolute right to your religious opinion. You may find, as many do, that this feeling has the effect of making it very unlikely that you will change your religious opinions. Much the same is true of politics and morality.
Another factor at play is that these are things that people care about. You may feel deeply offended that no one else likes your PB and anchovy sandwiches, but you are probably not going to find anyone willing to maintain an argument over the issue. This tends not to be the case with religion, politics, etc.
Insofar as these issues may actually be important, trading rationality for spurious certainty is a Bad Thing.
By eliminating labels that you feel you have to defend, you can have rational discussion on a wider range of things. This will also have a strong effect on the types of conversations you engage in, and eventually the types of conversation partners you tend to engage with; you will switch from more comfortable (and/or angry) conversations to more interesting conversations.
Sources and Further Readings:
Keep Your Identity Small by Paul Graham
Use Your Identity Carefully by Ben_LandauTaylor