I mix tap water with rain water routinely.
When I first started doing this I was using a fert that had 25% N as NH4 and no Ca so a source of Ca was necessary. But there is another thing going on here that depends on the fert and particularly how much NH4 you are feeding. At the time I was getting acidification problems and initially I was correcting this with powdered dolomite ... then I switched to tap water because it was easier to control pH without too much alkalinisation. That was a long time ago.
I now make up my own feed which is designed to accomodate a partial addition of my tap water. There are some issues with this and I can use my own strategy as an example to explain.
Without and with tap water I would be adding in ppm (aaN is total N from amino acids) ... the second row is with tap water (4% of total volume).
Ntot - 18.7, NH4 - 2.5, aaN - 3.1, NO3 - 13.1, P2O5 - 4.0, K2O - 6.7, Ca - 7.1, Mg - 4.9, SO3 - 0.9
18.9, 2.5, 3.1, 13.3, 4.4, 6.8, 12.1, 5.1, 2.8
So the big additions from my tap water (London) are Ca and S, so you need to check your local water analysis... mine has 120 ppm Ca but only 4 ppm Mg. So without tap water my fert Ca/Mg ratio is too low (by design). The tap water is also providing 11 ppm HCO3 which is 4.4 X the NH4 and so just enough to balance the acidification from this. If I increase the feeding I also increase the tap water in proportion, ... up to a limit... usually not more than 2.5 X the above, because my tap water also contains Na, Al, Cl, and I don't want these increased too much. So there are issues with adding tap water which can only be known from an analysis. So I agree with ***'s post above.
For a few years I used an all NO3 feed and no tap water, this was sort of OK but not all my plants were happy, ... and I noticed a significant improvement in going back to the mixture of rain and tap water and a NH4/NO3 feed despite the fact that I'm only using a small amount of tap water. So I wonder whether the improvement is all about pH and hence HCO3, or using a mixture of NH4/NO3, or whether Na and/or Cl are beneficial in small quantities or even the extra S ? All I am sure about is that the addition of tap water has improved things for me and provides a stable and flexible system for pH management. So for example with the limestone paphs I can increase the tap water % and with the barbata types I can decrease it a bit ... but I would not use any tap water with an all NO3 fert, especially in hard water areas e.g. south east UK, because in the absence of some acidification from NH4 the higher pH and Ca will just encourage scale build up in the long term.
My rain water, based on figures for the UK generally, contains at least a few ppm N and S and some of the other nutrients ... so there is a significant difference between using RO and rain water particularly if you're feeding at low rates. So for the figures above I've not included