There are two possible causes for your specific problem of muting adjacent open strings:
1 -Poor fretting technique
To avoid muting adjacent strings you need to fret with your finger tips not your finger pads. Fretting with your tips makes the first joint lie more perpendicular to the fingerboard and the pads will not mute the adjacent strings, Fretting with your pad makes the fingers 'lie down' (for want of a better term) and mute adjacent strings.
See how the LHS fingers are 'standing up' and avoiding adjacent strings? Compare this with the RHS pic where the fingers are 'lying down' across the strings.
NB: Also note how the hand is collapsed with the palm against the neck in the RHS pic, that is also poor technique. Both pictures show poor thumb placement, the thumb should be against the back centre of the neck whenever possible (sometimes certain chords and techniques will not allow this). Poor thumb placement makes proper fretting more difficult in most cases.
2 - Unusually wide finger tips
Your finger tips are so wide that even with proper fretting technique you cannot avoid muting adjacent strings. This is very unlikely and can only be remedied by a new guitar with wider string spacing.