Do employers silently discriminate against people who are speech disabled?

Do employers silently discriminate against people who are speech disabled? We all know that companies cannot discriminate by law on the basis of a disability (as well as age, sex, religion etc etc). But how do we know if people are effectively not doing that? We don’t. I am a stutterer and I put myself in the employer’s shoes. If they are interviewing someone who stutters they will most likely question the person’s ability to deliver presentations, engage with the company’s and external stakeholders etc, which are required at most office jobs. So they could think that hiring someone with a speech disability = hiring someone who can’t do the verbal communication side of things as effectively as they had in mind. Of course there is no way to prove that someone is discriminating, but that doesn’t mean that they don’t. I am afraid I am being victim of this at my company after being rejected for multiple roles after getting to the interview stage. I believe HRs professionals should better audit this process and look into ways to make it more transparent, like disclosing how essential the verbal communication aspect is in a job description and what adjustments the employer is willing to put in place for speech disabled people. Any thoughts/ related experiences..?