To write an effeminate gay character without being offensive, I say just write them with the same considerations as you would any other characters. I've met effeminate gay men and masculine gay men, and at the end of the day, the traits of being "effeminate" and "masculine" are just a single part of their personhood. These people I know are brilliant scholars, singers, writers, activists, professors, and all sorts of characteristics. They have lives and personalities that go beyond them being effeminate. When you write that effeminate gay character, ask yourself, how else would you describe this person? If the only thing you can come up about them is that they're delicate, pretty, and effeminate, then you should consider giving them other traits.
There's nothing inherently wrong with an effeminate gay man. Fact of the matter is, they exist out there, and the ones I know are strong-willed individuals, especially given how homphobic our country can be. It's all about making characters like them multifaceted people.
Also, I feel like this could also be addressed by having more than one gay character. If the only gay character is a highly effeminate gay guy who ticks all the stereotypes, then yes, it could definitely be bad optics. Even when you've given them enough of a personality and story beyond them being effeminate, sometimes people might not give you the benefit of the doubt. But having a diverse cast where they present differently, have varying personalities, lives, etc. will definitely help you out.