A wealthy businessman who leads a double life manages to accept his homosexuality only after discovering that his son is struggling with the same conflict.

In that case, the situation makes perfect sense, but I do think that information needs to be included in the logline, as the context is important.

1987, San Francisco Area in full AIDS period

Or perhaps he is a former teen heartthrob who has millions of adoring female fans but has kept the secret of being gay solidly in the closet out of fear of losing his fans.

You need to let us know what the conflict is. You should put the lead character in a situation where there would be people who would not accept his homosexuality. There would be stakes.
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"When he discovers his son is gay, but afraid to reveal his secret, a conservative Rabbi who has hidden his homosexuality, vows to reveal his secret to the synagogue but worries his congregation will reject him."
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In this, there is conflict because the lead might be fired for revealing he is gay, also in this we don't know how the story ends. What happens when he reveals he is gay to the Synagogue? It is left a mystery to be revealed by reading the entire script.

Hope this helps.

You are telling us the third act, you are giving away the ending.

In a logline you have a character, something happens that breaks up the norm, this causes conflict, and something or someone stands in the way of the lead accomplishing their goal; but you don't give away the resolution.

In your logline you let us know there is a happy ending. The lead character who struggled with being gay accepts it in the end.

My question, from reading the logline, is when/where is this set? Is it a period piece, set in a time when homosexuality was less accepted than it is today, or is it set in a a place where it is still frowned upon?
I think these things are important to know, because, my initial response is 'why do they struggle to accept their sexualities?'