Position of a star on the HR diagram Does the position of a star on a HR diagram depend on the magnitude system/color index used? 

I made a CMD of a particular cluster using HST WFC3/UVIS data, and when I plotted $F275W vs F275W - F606W$, a particular star (at a given RA and dec) was present near the blue straggler region, but now when I plot $F438W vs F438W - F814W$, this same star (at the same RA,dec) was found near the start of the RGB.

Why is this happening?
Does the position of a star on a HR diagram depend on the magnitude system/color index used?


Yes, of course. But note that HR diagram refers to a luminosity vs. effective temperature plot, while you're dealing with a color-magnitude diagram (or CMD).


  Why is this happening?


First of all, you should check that it's not your fault. If you see unphysical things, like the horizontal branch going beyond the red giant branch, you know you've messed up. This can happen with bad calibrations. But I think you're safe, it's not your case.

Then, I assume that the dependence of magnitude on filters is trivial.

Now, how colors change with filters?
Let's start in first approximation. Start imagining the Planck's function (here you go), and assume your filters are monochromatic. Recall that color is the difference of two magnitudes, i.e. \begin{equation*}m_1-m_2= 2.5\log_{10} I(\lambda_1)/I(\lambda_2)\end{equation*} where $I$ is the intensity and $\lambda_1&gt;\lambda_2$. Now take the points on the Planckian corresponding to your two wavelengths, i.e.  $I(\lambda_1)$ and $I(\lambda_2)$, and draw a line between these two points. If the slope of the line is negative (resp. positive), then the ratio of intensities is less (resp. more) than 1, and the color is negative (resp. positive). If the ratio is 1, then slope and color are 0. So color is somehow proportional to the Planckian slope between the two $\lambda$s. Here comes the point: color is most sensitive when the peak of the Planckian is near the wavelength of the filters. If the peak is too far from the filter wavelengths, then the Planckian slope becomes almost constant, and the color loses its sensitivy to temperature. That's the reason why in some CMD you see the bluer part of the horizontal branch suddenly going down: the color saturates and doesn't catch the temperature variations. First take-home message: different colors probe different ranges of the Planckian, and hence are sensitive to different ranges of effective temperature.

But I think we didn't hit the point. Going to the second-order approximation, we need to consider the whole width of the filter. This fact brings in a lot of effects. For instance, color excess starts depending on the star's spectral type. That is, hotter stars are more reddened, because reddening is more effective at shorter $\lambda$s (e.g. the famous Whitford's law), so early spectral-type stars emit most of their flux at short $\lambda$s. Another effect is that broad filters are highly affected by absorption lines and molecular bands, and I think this is your case. You have photometry in two broad UV filters, i.e. $F275W$ and $F438W$, of a putative blue straggler, so a source with a lot of blue flux. Moreover, the OH absorption band falls right in the $F275W$ band, while several CH and CN bands fall into the $F438W$ band. So your colors are not only proxies for effective temperature, but also for chemical abundances. Notoriously, the UV filters have been used to separate multiple stellar populations in the CMDs, exploiting their different abundances. So, second take-home message: reddening depends on spectral type, but most importantly colors can depend on chemical abundances.

Finally, as other answers have pointed out, the position of a star on the CMD can be changed by other effects, such as variability.