C (clang), 100 bytes

char *a,b[10],*i,*o;f(x,y){*b=*a;for(x=1;x<8;b[x]=a[y=index(i,o[x])-i],b[x+1]=a[y+1],x+=2);puts(b);} 

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char *a,*i,*o;c[4],x,y,z;g(x){x=x==82?0:x==71?1:x==66?2:3;}f(){a++;for(;z<2;z++){i=(z?o:i)+1;for(y=0;y<7;z?printf("%s%2X","#"+!!y,c[g(i[y])]):sscanf(a+y,"%2X",&c[g(i[y])]),y+=2);}} 

Creates a RGBA value in c[] array based on format i, then prints in o format

C (clang), 89 bytes

char *a,b[10],*i,*o;f(x,y){*b=*a;for(x=1;x<8;b[x++]=a[y=index(i,o[x])-i],b[x++]=a[y+1]);} 

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Takes input value in a, in format in i and out format in o. Returns out value in b

Minor cheat: storing result in b instead of printing to save bytes. Question doesn't disallow it.

char *a,b[10],*i,*o;f(x,y){*b=*a;for(x=1;x<8;b[x]=a[y=index(i,o[x])-i],b[x+1]=a[y+1],x+=2);puts(b);} 

char *a,*i,*o;c[4],x,y,z;g(x){x=x==82?0:x==71?1:x==66?2:3;}f(){a++;for(;z<2;z++){i=(z?o:i)+1;for(y=0;y<7;z?printf("%s%2X","#"+!!y,c[g(i[y])]):sscanf(a+y,"%2X",&c[g(i[y])]),y+=2);}} 

Creates a RGBA value in c[] array based on format i, then prints in o format

C (gcc), 181 bytes

char *a,*i,*o;c[4],x,y,z;g(x){x=x==82?0:x==71?1:x==66?2:3;}f(){a++;for(;z<2;z++){i=(z?o:i)+1;for(y=0;y<7;z?printf("%s%2X","#"+!!y,c[g(i[y])]):sscanf(a+y,"%2X",&c[g(i[y])]),y+=2);}}   

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Creates a RGBA value in c[] array based on format i, then prints in o format

C (clang), 100 bytes

char *a,b[10],*i,*o;f(x,y){*b=*a;for(x=1;x<8;b[x]=a[y=index(i,o[x])-i],b[x+1]=a[y+1],x+=2);puts(b);} 

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char *a,*i,*o;c[4],x,y,z;g(x){x=x==82?0:x==71?1:x==66?2:3;}f(){a++;for(;z<2;z++){i=(z?o:i)+1;for(y=0;y<7;z?printf("%s%2X","#"+!!y,c[g(i[y])]):sscanf(a+y,"%2X",&c[g(i[y])]),y+=2);}} 

Creates a RGBA value in c[] array based on format i, then prints in o format