Certainly in those days and many years after, open homosexuality was not accepted and probably punished. Nevertheless, many people in and out of the world of tennis either knew or suspected Tilden was a homosexual, but there was no effort to punish or ban him from tennis tournaments. Ty Cobb watched Tilden play one time and exclaimed “who is that swish?” or words to that effect. Tilden was still playing competitive pro tennis into his forties. He even played in the U.S Open at the age of 53 in 1946. Tilden was ostracized after being caught with an underage boy later that year and spent time in prison. Then he was shunned by the tennis and sports world. In the early ‘70s, Frank Deford of SI wrote a long article about Tilden.
Cobb maybe would have said that about any tennis player. DeFord says that the Tennis Association did know of the rumors and feared that they'd become public. Tilden had some mannerisms that could have bothered people.
I've also seen him compared to Michael Jackson in that people knew he was "weird" or "different" but didn't know more than that. And in both cases the pedophilia may have taken time to develop. Once Tilden had passed his prime his interest in boys became more blatant, and his activities eventually led to his arrest.
I suspect the wider public didn't know and didn't want to know. They could be unforgiving if they found out (or authorities who claimed to act in the public interest could), but aside from rumormongers there was a tendency to assume nothing untoward was going on. When nobody declared themselves as anything sexually or got caught in a compromising situation, there wasn't much interest in stirring things up.