If you literally put a line about dealbreakers in your main profile text, it can be quite offputting for the same reasons that the interview style dates are offputting.

Instead, write around the thing you want to say in a more positive way. For example: “I love to take sponteneous weekend trips. Where have you been last?” It filters out most people with fixed responsibiltites like kids and dogs, while opening up a conversation.

Or: “Unfortunately I meed to carry an epipen for when a cute dog does get to close. Fortunately my cat can snuggle with me all day”. Again, you filter the people with dogs, but provide an opening to people who are still interested.