It's something really serious to think about, not something to take lightly at all, so your concern seems reasonable to me while his lack of concern seems a bit reckless, in all honesty.
I think the side affects or adverse outcomes depend on social and environmental factors, your history, temperment, personality traits, other factors. If you have a supportive family, lower life stressors, good health, money, etc., you might fare better. However, keep in mind that while doing this work, if you lose your job, health, marriage, or something else, it could set you back much further as after your defenses erode, as you might now be living with the mindset from more of a position of vulnerablity rather than strength that defenses once provided. Of course it's ideal for maladaptive defenses to be replaced with healthier ones, but that takes time and I think the outcome has much to do with the skill of the T (yes, they have to work too).
The material that emerges could effect your confidence and your job. A demanding job is difficult while in this type of therapy, depending on your background, but also depending on other aspects of your life, such as health, money, having a partner to help with day to day activities.
Also, keep in mind some people here have 2 or 3 therapists and/or can go 2-4 times a week rather than the usual once a week or once every two weeks others can go. My ability to go only once a week really dragged out the process and I was stuck in depression for way too long and have not quite climbed out of it yet. I was flooded with dissociated trauma, and things happened on top of that, further weakening me. Now I'm very overwhelmed but too deep into therapy to just stop cold turkey. I'm climbing up the mountain, but avalanches keep coming down, and I'm getting worn and weaker.
Be careful. Read about "ego strength" and psychodynamic therapy. Note that the stronger your defenses are now, the weaker you will be underneath. People may disagree with that. Some have defenses like a brick wall, but whether or not they crumble can depend on your therapist/the type of therapy you are in.
I just realized your user name; given your name is WorriedWell23, I wonder if what I said is even relevant to you. If you don't have a history of trauma, neglect, abuse, the side effects may not impact you as much as someone who had very poor parenting with abuse, especially before the age of 2. Preverbal trauma changes the way your mind works, often leaving you with fragmented sense of self, which its much more difficult to get through therapy with. It can be volatile, which can really affect your career.
Hope I didn't say too much.