Inconsistencies pop up during writing and role playing. Really, writing and role playing can be considered two sides of the same coin and when doing fan-fic and role playing with already created and codified stories that have their own canon, conflicts will happen!
Alternate Versions
When doing dice-based role playing usually there is a book the codifies how everything works and a game master can decide how to bring in elements from other books. This kind of direct translation is an easy way to bring in opposing elements. This is what has been done here with such things as the Falcon Class Starship which is, of course, the YT-1300 cargo ship from Star Wars. There is no real way to say this isn't borrowed from Star Wars, so don't bother. In some areas this sites puts a hat on thing. By that, I mean it is noted that the design was based on... Insert origin of the idea here. This allows a writer to take the idea, reshape it in an entirely new way that works for the story being done, and use it.
Timeline
As with the 2009 Star Trek reboot, if a person wants to completely re-do something in their own way the creation of an alternate timeline can be used. This creates an entirely new version which can be shaped, reshaped, and altered to suit specific purposes, which is what is done here with ideas from Stargate. It was impossible to reconcile most of the story elements of the Stargate franchise with Star Trek which is largely the canvas that Solas Tempus is painted in. So, while it hasn't been explicitly said, an alternate timeline is created where we can make it work.
Credibility
This kind of taking an idea and reworking it lacks a certain amount of credibility, and when using it, a person should be aware of this.
Melding Versions
Most of Solas Tempus takes place in the 24th century which interludes into other times. It is also noted that there is a multiverse with infinite realities. In a Doctor Who crossover with Star Trek done by IDW Publishing they created a reason for two alternate realities that would normally be incompatible to reside with each other so that The Doctor could appear on the Enterprise. They also made a big deal about putting a hat on the fact that these two universes were incompatible and leaving them merged would cause serious problems. This is a great way to handle temporary bridges between different storylines. Two realities, merged by some event, and then the game or story goes into writing things to the way they should be.
That isn't the only way to do things, however.
More Similar Than Different
Magic and magical items have been introduced to Solas Tempus, originally with the Solar Crystal. Other items were introduced as well which fall under the 24th century care of Animas Tempus which studies the unexplained. This creates an architecture in Solas Tempus for describing items as magical and having incredible abilities which are not covered by science, even within the nearly limitless bounds of what can be done with Star Trek.
A magic item from Angelic Sins can be used in both story lines because Angelic Sins takes place almost entirely in the 20th and 21st centuries. Solas Tempus takes place in the 24th century so it is conceivable that (since we adhere to the idea of the multiverse) the same item, with the same properties, and at least similar history can exist in both places without too much trouble. Since the two settings done directly conflict, someone wanting to use a magical item can look at the description of the item and toss out the bits which don't make sense. A good magical item description on the wiki should be made in such a way to allow the item to be used in different settings, if possible.
Someone looking at an entry that lists a history going from the 19th to the 24th centuries need not worry about anything beyond the time period they are playing in. Similarly, a person could make a note about a split in the history of an item, place, or some such which dictates the differences in between two universes leaving the rest of the entry the same.
The Hat
The term of put a hat on it comes from the idea that the writer lets the audience know that they realize something is overly convenient, strange, or somehow obviously a tool. This idea breaks the 4th wall but lets the audience know the writer is aware something has been fudged or otherwise resolved in an obviously unskilled. Letting the audience know that the writer is aware something, perhaps, might have been done better with more work or just doesn't mesh very smoothly can allow the audience to move past a glaring issue and enjoy the rest of the plot. At the very least the writer doesn't come off as being unaware that some of the writing could perhaps use improvement, more work, or was just plainly difficult to accept.
Conclusion
Try to make things work out, make sense, and mesh well. But don't sweat the details if you don't have to. Have fun with it, put a hat on it. I like hats.