Over 35 need special permission to fight?
Isn't that age discrimination?
Sort of. Let's say I was 35 or older and I had to make a special appearance to get my license and I had the same thought as you, and decided I was mad enough to sue.
I would have to sue under the fourteenth amendment, and I would sue under what's called the "equal protection" clause.
Equal protection isn't, however, absolutely guaranteed to everyone in all circumstances. Basically, depending on what basis the government differentiates between people, they will have to meet a corresponding level of "scrutiny" to justify their doing so.
Different treatment under the law on the basis of race, alienage, religion, or national origin is held to the highest level of scrutiny; the government has to show they have a compelling state interest, the law has to be "narrowly tailored" to serve that interest, and there must be no less restrictive alternative. As far as I know, only one law EVER made it past this level of scrutiny: Korematsu vs U.S., the almost unanimously wrongly-decided case that held it was OK to intern Japanese Americans in camps during WWII.
If a law discriminates on gender, there is a middle level of scrutiny called "intermediate scrutiny" which requires an important government interest and the law must substantially further that interest. Differentiation on sexual orientation might fall in here too.
But ALL the rest, until the courts say otherwise, only need to meet rational basis review, which is the lowest standard of scrutiny and VERY easy to meet. All you need to show is a legitimate government interest (which safety of athletes clearly is, otherwise the athletic commissions wouldn't exist) and a rational relationship to that interest (which merely means you could make an argument for a relationship existing.) Requiring a license for fighters after age 35 is arguably related to fighter safety. It doesn't need to be irrefutably related, and the relation doesn't need to be strong and direct in order to pass rational basis review.
So basically, YES it is discriminatory, but no, there is no chance in hell you'd ever convince a court it violated the fourteenth amendment, so the law remains until and unless the legislature decides to change it, which of course is very unlikely.