A triad, major or minor, should not come across as dissonant, in open or closed position. Both will contain the same three note, name-wise. It's just that in closed position, those three notes are as close as possible to each other - CEG, EGC, GCE are the only options, whereas in open voicing, they could be played with appropriate notes missing - CGE, for example ( the E is an octave higher than it would be in closed position.
So, first to establish is major or minor? That's fairly simple - the sound between C and any E will be the only deciding factor. The G note won't affect which is which. So, basically, after that's established, given that you can recognise that out of the three, the root is C (it certainly won't be E), but could be construed as G. But - if you thought the root was G, then its third would be B, and there wouldn't be a B in that particular triad.
I think the problem could be that you hear E and G together. That in itself does produce m3. Fooling you into considering that it's a minor chord. But, were that the case, there would be a D note somewhere (5th of root G), and there isn't.
The one that gets a lot of folk is the major 7th chord. As the lower 'triad' is major, but the higher is minor. And that's in closed voicing!
Playing loads of chords in both open and closed, as strummed but also as slowly arpeggiated, will give you more opportunity to unravel which notes are used. It'll also fortify you knowing where the notes actually are on either guitar or piano - the two most common instruments on which chords are played.
An afterthought: have a go at singing the intervals involved. R>3, R>5. A third (R>m3/M3) will obviously be smaller than a fifth (R>P5), and the difference when singing those notes should make that apparent.