"Normal" is a subjective and relative term — something can only be described as such in relation to a "norm" or standard. When you use the word "normal" in this way you may appear to the reader to assume that you both share a similar idea. Or you may sound critical or disapproving of the idea of normality. The words "conformist" or "conventional" sound more objective.
Your words "cannot bear to be" suggest that you may be leaning towards the less objective side. "Obsession" can sometimes have a positive connotation( "passion") but more commonly denotes an unhealthy state of mind.
I can't think of a single-word term for what you seem to want to say. These are some possibilities that come to mind, and they could be recombined with each other:
- obsessively conventional
- obsessively conformist
- obsessed with not standing out
- fearful of standing out from the crowd
- anxious to be thought of as "normal"
- over-concerned with following convention
Personally, I lean towards 1 and 2, although 3 might fit if you want to express some personal disapproval of the idea of normality.
