Samples of red giant branch (RGB) stars have been compiled from the literature for seven moving groups, and searches made for both GALEX FUV and Johnson $\mathit{BV}$ photometry. It has been possible to derive a colour index $(\mathit{FUV}-B)$ for many giants, which has been combined with $B-V$ to give a two-colour diagram for each kinematic group. In addition, analogous data have been gleaned for a small number of red giants in the open cluster NGC 752. Optical photometry has been combined with parallax and proper motion data from the Gaia DR2 data release to document the colour-magnitude diagram (CMD) positions and space motion velocities among the proposed group giants. Comparisons with isochrones confirm a range in age among the groups considered. However, none of the group samples evince RGB sequences as tight in the CMD as those typical of open clusters. Considering also the velocity dispersions found within each set of group candidates, it is concluded that the fraction of non-members included may be significant. The RGB stars ascribed to different moving groups are largely located within overlapping regions of the FUV two-colour diagram, without any obvious systematic offsets between groups of different age. All of the RGB sequences attain a maximum $(\mathit{FUV}-B)$ colour of $\approx 14.2$ –14.5 mag within the optical colour range of $1.0 < B-V < 1.25$ . Many of the stars in this range are in the core-helium-burning (CHB) phase of evolution. On the red side of the CHB region in the two-colour diagram, i.e., at $B-V > 1.25$ , the RGB stars from different groups largely map out a common locus. Among CHB and other giants blueward of $B-V = 1.25$ there are a number of stars with FUV-excesses ranging from 2-4 mag as judged by the $(\mathit{FUV}-B)$ colour. There is found evidence for a range in chromospheric activity among CHB stars. By analogy with known properties of Hyades cluster giants a range in activity among the CHB stars within a moving group may be a consequence of different degrees of spindown corresponding to different amounts of time spent in the core-helium-burning phase.