The notion of white and colored noise The autocorrelation function of AWGN is an impulse response at t=0, and its fourier transform or its spectral power density has a flat infinite BW

Now any receiver will have bandpass or low pass filters that will limit the noise BW

Does that mean that in reality we are actually dealing with "colored" noise and considering noise to be "white" within the filter BW is an assumption made for convenience purpose?
Yes. 

However, if you are dealing with a discrete-time signal, if your A/D is proceeded by an ideal low-pass filter with cutoff frequency $F_s/2$, with unity passband gain, the output power spectral density before sampling is:
$$
S_y(f) = |H(f)|^2 S_x(f) = \frac{N_0}{2} \operatorname{rect}(f/F_s)
$$
This means that the autocorrelation of the filtered noise will be:
$$
R_y(\tau) = \mathscr F^{-1}\{S_y(f)\} = \frac{N_0}{2T_s}\operatorname{sinc}(\tau/T_s)
$$
where $T_s = 1/F_s$. If the noise is zero-mean, Gaussian, and sampled at time instants $t_n = n T_s$, then each sample will be uncorrelated, and since they are Gaussian, will also be independent.   In this case, in the digital domain, the power spectrum will be flat for all frequencies. 

This is not the only way to generate noise that is white in the discrete-time domain, but is one way, albeit a physically unrealizable one.