Well that's one hell of an alarm bell....
If you're desperate, I'd say take the job if you're offered it but be prepared to have one weird boss. I'd be applying for new jobs from the day you start. If you're not desperate for a job, then maybe go to the second interview because you have not go much to lose, but don't be off the mind that you'll accept the job if you're offered it unless something radical changes.
My weirdest interview experience has been when I once got a telephone call about a recruitment job I had apparently applied for. I was unsure what job they were referring to so I decided to buy some time and asked if they could re-arrange the interview for tomorrow morning. I cancelled going out to the pub that night, racked my brains as to what job it could be, drew a blank, and in the end decided did some very general interview prep and decided to try and wing it.
She called me back in the morning. The first question was relatively straightforward- why did I want a job in recruitment? I answered it all nice and politely, but then she asked about my work experience. She told me that my student job as a tour guide was not a "proper job" and demanded to know why I had not found a "professional job" as a student. She didn't think the one summer I spent working in a restaurant as sufficient either and strongly implied that I lacked motivation.
I dropped my friendly veneer at that point and told her that I had no idea what job I was being interviewed for as I had not made any applications in recruitment. I then demanded to know where she'd got my CV from. She told me it was just on her screen taken from their database, so I told her very sternly that there's been a misunderstanding and asked her to remove my CV from the database as I didn't appreciate getting unsolicited phone calls and being interviewed in such a rude manner. That shut her up.
In hindsight, what probably happened was that I uploaded my cv onto some job site and ticked a box that said I'm interested in recruitment. The moral of the story I think is don't say anywhere that you're interested in recruitment, or sales for that matter, I think both are just dodgy areas to work in.