It's Tommy we are talking about, not Rusty. For me Tommy wouldn't care if something that is shameful or negative for others is being associated to him, like him having STDs, him being poor, him being an asshole etc Every single one of these he would dismiss and ignore, it does not bother him nor does it hit him.
But being sentimental? Being less of a raging asshole? Maybe being seen as someone vulnerable and/or caring? He would hate it. He hated it during the whole game when the MC tried being considerate of his feelings, always saying that "He don't need to care for his fucking feelings so much". That's basically the only thing I can see Tommy being ashamed of being... being more human, just like Quinn and just like Lily.