I wouldn't say it will be detrimental, but you will find it harder to land a job. When doing hiring at my previous three companies (two corporate aviation, one airline) it was always stated in the interview that we were not looking for a first officer, but rather a future Captain. I will grant you that borders on HR gimmicks given that we were very much hiring a first officer, but it was never with the expectation that person would stay in the right seat. We very much looked down the road as to whether the person had the ability to grow into a future command position. We did hire pilots with varying medical restrictions, but it was always on a case-by-case basis, and we were not always able to award a position to a pilot with a restriction because of the job requirements. So, my first suggestion is that you don't apply to a company that you know does single-pilot ops. That sounds obvious, but I've seen pilots apply to an airline where that pilot had a "no night flight" restriction on their medical. You're now restricted to applying to companies where you know they fly two-crew. In the airline world that's not a problem, but many business aviation operators fly single pilot ops, so you'll have to do some research before you send in your application (which you should be doing anyways!). My only other suggestion is that you look at your other skills and what else you could do for the company you apply to. A two-crew airplane requires an FO, but if they can't make you a Captain in the future, that limits what the company can do with you. So remove that limitation for them. Could you teach, could you help with manuals, or safety, or something else in flight ops? What else do you bring to the table other than flying? Many pilots will add those skills in to get them ahead of the competition, but you will have to lean on those a lot more than someone else. It'll be a longer road, no doubt about it, but it's not impossible.
The big thing is to keep your head up. You will likely see a few rejection letters, but understand that it is purely a business decision. Take the rejections with grace, thank them for entertaining your application, and eventually you'll land somewhere. Who knows, you may find that it is through one of those rejections that you ultimately find a gig, so stay professional and something will come your way.