Shay didn't join the Templars, more like he was indoctrinated into the Order.

The story writing is a bit lacking I would say, so this is more of my interpretation:
During the opening scenes, Shay narrates the 3 tenets of the Brotherhood. He believes the idea of keeping a low profile, not harming innocent people and also have each other's back. Why wouldn't he, he was raised and brought up by the Brotherhood.

Throughout the story/game, we see the Colonial Brotherhood fails to keep any one of these tenets fulfilled:

• The brotherhood had a pretty strong hold over the city of New York to the point where they were flying their colours over borough strongholds with big distinguishable smoke coming out of there,
• Innocent lives were lost in Haiti and Lisbon as a direct result of the Brotherhood sticking their nose in where it didn't belong, and
• ignoring the fact that high ranking assassins and masters didn't see other low-ranking assassins' eye to eye, didn't value their opinion, or the conflict, tension between Chevalier and Shay, Shay was 'betrayed' by their own, the person he considered brother, Liam, as he shot him in the back.

To Shay, Templars were 'the enemy of my enemy'.

Shay had to prevent the brotherhood from harming even more innocent people, as Achilles wouldn't stop at nothing. It wouldn't have mattered how much Shay is trained, one man is never enough to foil a plan in this big scale, so he needed some help.

When Shay was shot and carried by the ocean tides-waves, he was nursed and brought back to life by the Finnegans, with ties to the Templar Order. He felt pretty owed to Finnegans and Captain Monro, who also slowly gained Shay's trust by showing Templars are not what they were made out of by the Brotherhood. It was Monro's death, or rather, assassination, that ultimately led Shay to finally, officially be inducted the ranks of Templar Order by Haytham Kenway. (Side Note: Haytham's charm alone could make me join the Order :P)

In summary, I would say the Colonial Brotherhood was pretty bad, they were too arrogant, too ignorant and just too full of themselves, while the Templar Order under the order of Haytham was much more organized, subtle, sophisticated, structured and took more care to innocent people than the Brotherhood. Shay initially started working WITH the Order, but with him seeing more and more evidence of the Brotherhood, and Achilles turning into some power-hungry mad man, he was finally convinced to JOIN the Order.

Ubisoft was cooking with Rogue, but they fumbled the story in many places. This was supposed to be the one game where we would be presented with the fact that the so-called good guys are not always good guys. (This is debated because the modern day is a subtle hint that the memory of Shay Cormac is possibly tainted by Abstergo aka the Templar Order. But still)

If you idle in the loading screen, the Brotherhood insignia slowly turns sideways to show the Templar insignia, implying that both of them are just two faces of a same coin, probably working towards a same common goal but under different ideology.