Is learning one style of filipino martial arts such as modern arnis presas method with one teacher who you started training with first and also taking other styles such as Kali and Balintawok at another school disrespectful to the first teacher?
It depends on the teacher, but generally the answer is no, it's not disrespectful.
The best teachers I've ever known had no problems with students training under other teachers. Many, if not most, even encouraged it.
That said, you should ask your instructor first before doing anything. Maybe phrase it like this: "Hey, I'm thinking of taking classes under so-n-so for a while to see how they do things and to expand my knowledge. If I did that, would that be okay with you? What do you think of that idea?"
If you get told no, you can't train there while training here, then just ask why. Ask what the concern is. Usually it's because the styles are so similar that your instructor might be concerned that you'll get confused and start mixing up styles. Other times when I've seen this happen is when a student asks to train with someone that the instructor knows and whom he/she thinks has a bad attitude or teaches the wrong way. So they want to keep you from making a mistake.
Of course, sometimes it's just because the teacher doesn't want to lose a paying student, especially not to a competitor.
Personally, if an instructor told me no, I'd be more concerned about that instructor than anything. I'd probably consider leaving. A good instructor doesn't worry about students training with others. They're secure with what they teach, and so they don't worry that students will train elsewhere and discover that they've been taught poorly. Only the bad instructors will worry that, and it's because they know that they themselves aren't that good.
So anyway, just ask. Martial arts are a small world. Eventually word will get back to your instructor that you're training somewhere else also. And you don't want to tip-toe around the issue and get all anxious about it, letting it build and build, so just go ahead and ask your teacher if it would be alright as soon as possible.
Hope that helps.