Simultaneity is real in precisely the same sense that the component values of a vector or tensor are real: your instruments will certainly measure certain things as co-incident and those measurements are real and instruments can measure vector components. But these events are not needfully co-incident in other inertial frames, just as the component values of a vector will be transformed. However, the descriptions from different inertial frames are equivalent - they convey the same information and are linked, in SR, by the information-preserving (i.e. bijective) Lorentz transformation.
How can you say that you are simultaneous with a star fleet coming from Andromeda, if there is no way of knowing it ? For simultaneity to be meaningful, shouldn't it propagate at the speed of light ?
For events in Andromeda - or other far off events, you can only declare their simultaneity relative to your inertial frame of reference after "betokening" or "announcing" information reaches you. So, from your inertial frame, you can only conclude that a radioactive decay at your position was simultaneous with some event in Andromeda "announced" to you by the arrival of e.g. radio signals 2.538 million years afterwards. So in this case, your declaration of simultaneity of the decay and Andromedean event can only be made 2.538 million years after you observed the radioactive decay.
The Rietdijk-Putnam argument (I wasn't aware of Rietdijk - I knew Putnam argued this way) is simply making a case for eternalism: it is most decidedly not a paradox in the strict sense of being a logical contradiction. It's simply saying that in the light of relativity, the reality of an event or thing cannot be restricted to a single instant in time: everything must be thought to be a four dimensional object with a real, nonzero extent in spacetime for special relativity to avoid logical contradictions. Other names for someone who subscribes to this kind of philisophical position are Detenser, Eternalist, Perdurist and Four-Dimensionalist. I should declare my own position as being decidedly eternalist.
Your question and line of thought are very keen and insightful because they allow you insight into why simultaneity can be frame dependent and yet not beget logical contradictions. It is because there is no way of instantaneously communicating or comparing experimental results between distant observers. When one takes account of the lightspeed limit in bringing together experimental results for comparison, it is shown that no violations of causality are possible: even though relatively moving inertial observers may disagree on the time between two events at the same spatial point, they will not disagree on the sign - if one event happens before the other in one frame, it must do so in the other. Be careful here: in general Lorentz transformations do indeed alter the order of events, but they do not re-order events at the same point (see footnote). If event $A$ can be causal of event $B$, all inertial observers will deduce this relationship.
Footnote: A word of warning: you may see some authors (although not ones talking about SR alone) talk about Lorentz transformation as meaning any transformation from the group $O(1,3)$. This includes transformations that invert order of events even at the same spatial point. A subgroup of $O(1,3)$ is the topologically connected component $SO(1,3)$ or $O^+(1,3)$ containing the identity. This contains only orthochronous ones - ones that do preserve order at the same spatial point and it is this one that we talk about in special relativity. I've seen many Wikipedia pages use the more general usage, although I don't think any talking about SR do this.