If the meson contains a quark and an anti-quark pair of same flavor like c quark and anti c quark in j psi particle or s quark and s anti quark in phi meson then color of quark and anti-quark must be opposite like blue anti blue etc because particle and its anti particle have equal and opposite electric , color charge etc.

But for mesons containing different types of quark anti-quark pair , I am not sure. I think color of quark and anti quark should also opposite here so that mesons become color neutral....

Every observable object must be colourless (colour neutral), no matter whether it is a meson or a baryon. There are essentially two ways in which hadrons can be colourless: they either contain three quarks, all of different colours (or three antiquarks), or they contain a pair of a quark and antiquark of the same colour-anticolour. The three-quark (or three antiquark) hadrons are called baryons, and quark-antiquark hadrons are called mesons. Actually, it is possible to have hadrons consisting of two quark-antiquark pairs (tetraquark), or of a combination of three quarks and a quark-antiquark pair (pentaquark). They all will be colour-neutral. However, there is no convincing experimental evidence that tetraquarks and pentaquarks exist, despite some intriguing observations.

Yes, mesons also have to be color neutral. Otherwise strong interaction between mesons would be a long range.

"Color neutral" means if the system is seen from distant, the net color is 0. This is just like the case that the electron and proton are charged, but hydrogen atom is neutral.

Mesons consist of quark and antiquark. So the color structure is color and anticolor.

To be neutral, the color state is something like Red-antiRed, not Red-antiBlue.

For baryons, the mechanism to be neutral is a bit different from the case of mesons. In baryons, the color structure is something like (RB-BR)R+.... This means reaction diagram of RBR is cancelled by the diagram of BRR because of the negative contribution and the net color charge effect at a distance is 0. This color structure of the baryon also shows antisymmetricity of the color part of the baryons.

Sorry, I made mistake. (RB-BR)R should have been (RB-BR)G, RBR ==> RBG,

BRR==>BRG.