Without knowing the specific details of what info you want to gather, a couple things come to mind:
Be clear about what you are asking each question
If a user thinks they are only being asked about certain info for marketing purposes, they may a) be less likely to provide the info and b) feel less positive about signing up for your site. Sometimes you will see forms that say, "Why do we ask this?" to explain what the reasoning is. For example, a sign-up process might ask about your gender, then say "We ask this so we can use appropriate pronouns across the site." I think a user would be more inclined to provide this information if they see why it benefits them.
Make information optional when possible
Some pieces of information, like a username or password, are obviously required for signing up. But I would restrain from marking truly optional info as required. While it might benefit your site to collect demographic info, any extra requirements could decrease the number of people who finish the process, especially if they feel pressured to include information they don't want to reveal.
Neither of these are necessarily exclusive to a site with sensitive info, but there's a chance of each effect being amplified, since users will likely be more hesitant to divulge any details.