The IRS in the US has rules that designates things as taxable income or not for many of these questions. Businesses can still reimburse regardless of IRS categorization, but you may be taxed on the reimbursement as income.

To avoid that issue, most businesses will avoid reimbursing for incidentals that should be considered income. Suits or standard office clothing, I believe, are taxable in most circumstances. Uniforms are not. Of course there's lots of grey areas that keep accountants in business. I'd assume yoga would count as an exercise allowance and not be taxable, but that's just a guess.

Safety-related clothing is also deductible. When I worked in the oil business I could deduct things like steel-toed boots, overall, gloves, etc. off my taxes (or the company could have provided them for me as a business expense). At the same time, as you say, even if I only wear a suit for work, it's not deductible. Such is the simplicity of our tax code :-)