"I have had sex with X number of dudes" - doesn't sound all that gender neutral.
Same with 'guy': "how many guys have you kissed" isn't asking the same question as "how many people have you kissed."
"How many dudes do you live with?" isn't gender neutral, if you think it's just an intimacy thing. How many dudes were at the party? It isn't intimacy, intimacy is just an interesting way of making homophobic men confront the "dude isn't gender neutral" argument though.
So, what's actually happening in that 2nd panel? By all means, use dude how you like, just be honest about it.
I have, a couple of times, made men live their "dude is gender neutral" truth. Turns out telling people they are married to a dude, went to a party and kissed that dude one time, asking about their 2 dudes they have for parents, isn't such a great time for them. Just be honest about it.