During the Middle Ages, sodomy designated all sorts of sexual behavior that had no reproduction purposes, so the variety of practices that covers is wide and is not the practice we imagine nowadays, where it is mainly assimilated to anal sex.

As for the reality of the allegations, the Templars being made of men only, there may have been instances of sexual acts between them, even though it would have constituted an offense that could have led to sanctions against the brothers that committed it. It seems however unlikely that it was a common practice, as the charges of heresy (specifically of idolatry) were never sufficiently proven (no idols were ever found, for example) to give much weight to the rest of the charges.

The reasons for the importance and seriousness of the charges were that Templars were a problem for the King of France at the time, as they were placed under the direct authority of the Pope (with whom the King was in regular conflicts over political and religious matters) and that the loss of the Holy Land 20 years before meant that they were more present than ever in the politics of the West. Plus, their order was extremely wealthy, at a time where the kingdom of France was in dire needs of finances. So there was several reasons for the King to have them disbanded.

This is why a lot of the accusations against the Templars were for some part exaggerations, witness accounts from Templars who had been rejected from the order, lies invented by the French (as they did in several other instances of such trials, it seems), or "admissions" by some Templars themselves during torture (at the time, the Church even expressed concerns that the admissions could possibly have been affected by the tortures, as the trial lasted for 7 years, during which the knights were imprisoned in France). Some accusations may have been true, but it's now difficult to assess how much of the accusations were actually based in reality. The Templars were a very discreet order as to their internal operations, so it's possible their long time in the Holy Land had brought them to instances of practices not fully in line with what the Church defended and we have now difficulties in determining to what extent this is true. In any case, the idea of the French king and his counselors was to have something so serious the Pope and the Church would in the end be pressured into forsaking the Templars.

TL;DR So yes, in large part, it was certainly due to political reasons to see the Templars disbanded, but there may have been instances of homosexuality in the order.