This is the question as I understand it:
If your song is centered on E major as tonic, and you use the major chords E G A C and D in your chord progressions, it seems to mix modes in a certain style that can be found in many pop songs. Is there a name for this style?
I agree it's a common style, and the guitar's open-string chords seem to produce that style automatically. Or at least, when I picked up the guitar at age 11 when I had a chance and nobody was around, and I started to find chords without knowing anything or having any books or anything, simply by trying to put my fingers like I had seen guitar players do, I found the chord progression E - G - D - A - E in a matter of a few minutes. I didn't know the names of the chords or anything, but I liked the sound of it a lot, it felt very fascinating and different from songs I was playing by ear on the piano. So from my own anecdotal evidence, it's justifiable to say it's guitar-based. It's almost as if it was a built-in preset sound in the guitar - just pick up the instrument and that's what comes out by itself.
It took me some years to translate the style to my piano playing and find ways to reason about what was happening with the chord progression: it seemed to move between keys E major and E minor in a fluent way. And not studying music in any institution, it took decades to find out that there are actual names for that moving-between-keys fluidly. One of the words is "modal mixing", like you suspected. Playing a chord from a different mode makes changes to the harmonic context, and this can be called modal mixing. For example going from the E major chord to G major toggles the sharp/natural/flat switch on the G scale position from sharp to natural. And eventually getting back home to E major returns the switch to sharp.
If I compare the style to playing the piano, in my subjective experience, the piano somehow tends to encourage staying inside a key and not do too much modal mixing. I can only guess where that difference comes from, but maybe it's due to having to concentrate on seeing the scale of the key on the piano keyboard, and changing that to a different scale feels like a more serious thing than on the guitar. When playing guitar chords you don't even have to think about what your scale is. You just play your chords and let theory guys analyze it later!
One characteristic trait in this guitar-based style is the lack of or avoiding the so-called leading tone, which in E major would be D#. Likewise, the B major chord is not used. If you'd like to play a B-based chord, B minor would fit the style better. Playing or singing a D# would feel like a breach of style here, unless you do it in a bluesy way, alternating somewhere between D and D#.
However, I'd like to claim that there's a simpler and less fancy name for this style. It's actually shown by Youtube if you have captions on:
It's called rock music.