This won't be a popular answer, but if you are talking about technology startups in Silicon Valley, then the answer is yes, you probably are hurting your chances.
Silicon Valley has a peculiar and yet virulent bias against the suit. It's even a euphemism for an overly conservative, corporate-buzzword-speaking, pointy-haired Dilbert boss. No one wants to work with an "empty suit". Software engineers help strongly define the culture in Silicon Valley, and they overwhelmingly don't wear suits, or in general they don't want to work with people who do.
There are exceptions (Siebel was a notable example of a culture that emphasized the suit). But you will even find at large companies, unless you are interviewing for a position in sales or finance, that you will hurt your chances in a suit.
For younger people looking for jobs in small to mid-size hyper-growth companies, a suit has also come to imply a lack of prioritization. You spend too much time on your clothing, which will not impact business success, and too much time on appearances.
Startups are notoriously contrarian cultures; they are looking to change the status quo. Dressing in a suit represents the status quo, or at least, a caricature of it. This, of course, leads to an ironic conformity in how people at startups dress.
There is also a strong signal of lack of confidence in wearing a suit. The implication is that you wear a suit because your skills are not strong enough on their own to justify your employment. You might find that engineers in general are proud of the fact that their skills are so valuable that they can find gainful employment where they don't have to wear a costume. A suit reminds people of what young high school or college students might wear to appear grown up.
Probably the most damning thing about the suit in this context, however, is the appearance of being tone deaf or difficult. You know, as does everyone, that no one wears a suit at a tech startup. But you wore one anyway. Either you don't realize that this isn't acceptable, or you are some form of suit activist. Neither sounds that appealing in a new hire.
If it isn't obvious from my tone above, I am not justifying this rationale.
However, for your LinkedIn profile, if you are looking for a job at a hyper-growth startup in Silicon Valley, I recommend business casual dress for men and women.