This sounds like interesting research, and necessary as well. You will, of course, need to run the research proposal past your Internal Review Board, who will judge whether your questions pose any harm to the respondents. I think a key might be providing respondents with a confidential contact that they might avail themselves of in case they are discomforted by your questions.
I think whether or not it's unethical will depend on how you frame it. In general, looking at the intersection of identities between race/ethnicity and sexual orientation or gender identity isn't unethical. It's necessary, important work that prevents us from missing nuances and difference of experience. Not attending to the intersection of race and LGBTQ identities risks designing public health interventions that aren't appropriate for those who are most marginalized. An important piece of doing this well would be allowing folks to self-identify their race and their sexual orientation and gender.
Perhaps you could do a pre-research questionaire, or discuss with a group such as Imaan (LGHT Muslim group), London Queer Muslims, Sabah Choudrey (Colours Youth Project), African Rainbow Family, Naz, Sarbat LGBT Sikhs, Nas and Matt foundation, UK Black Pride etc
This way you could assess how best to approach the topic, and find out what the community themselves would like to be heard.
I see that you are in Canada, so there may be more appropriate local groups to contact, but these might perhaps be able to help with this.
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