They will, of course. That's a part of it, but not the whole picture. Don't forget the text's perspective of an external watcher, it often says "it seems like", not "it is so". That of course leaves you some freedom, so you CAN play fanatic lizzys, but it's not intended to forget the rest of it completely. You can't just pick parts from the background descriptions that fit your idea and forget about everything else. For example, you really have to read the god's description that belongs to a religion to really get the direction of it, not just the creeds or races description. Well, that doesn't count as much for the creed descriptions that enable LOTS of gods - still, a follower of a certain god will like his patron's personality and may strive to act alike, just from the related teachings.
Imagine above said lizard-ish dedication in a religion of one of the elder gods in the world illarion, not something like christianity or islam or any other (expansive) religion of our world.
The elder religions in illarion aren't expansive, not "radical". Tanora didn't teach them that all other religions are wrong - in fact, no god of a pantheon that consists of many gods is too likely to do that - and it's also nowhere mentioned that they see anything as "heretic" and have to eradicate it because of that. In fact, a big point of Tanora's description is "wise".
Please take a look at Tanora's description. And then take the extended description of the lizard's creed as add-on to that ! That's how it's supposed to work. And that will kinda clarify everything related to it. There, you will find that some followers can look like fanatics, always ready to smash everything truly evil or related to it, but it clearly says that the biggest part of her followers are of peaceful nature. Don't oversee that !
Hint :
Of course it's quite an effort to play a lizzy who is raised to be kinda peaceful or even open minded, and still believes in his fixed religious principles. And when it comes to stuff that is unjust and "evil" his views become so fixed that he seems to other people as a fanatic : "An undead ? RRRRRrrrrrrrr.... Glory for the goddessss !" (Insert "SLAY HO !"(tm) action here) - even the most cultivized lizzy could turn into a whirlwind of claws, tail and steel.
But that kinda ends up in a certain degree of mastery or roleplaying, thinking out-of-boxes a bit, and i admit, you can't expect that much thinking and acting from most people. And of course, you can't expect from nowaday's players to read everything related to a certain theme if they find one part they like, so i sometimes really wonder why i bothered about writing all that stuff. *g*
You can always play as you like, you are not forced to read anything of the background here (which is, in my view, one reason for the fact that most races don't really have race-rp), but don't expect other players to adapt to your views either if they like to focus on another part of the descriptions which they like better.
Anyway, the lizzy i sometimes play is quite fanatic as well, but mainly because he uses to be kinda plain dumb and expects anything unknown to perhaps be kinda evil. But on the other hand he can be as harmless as a lamb when it comes to people he knows as not-evil, or give him tasty fresh fish.
But ! That still doesn't mean that the whole race is like him.
Remark : To understand and get the whole picture of a story or a description, you have to read the whole, in the order it was written in. Else you will miss important parts.
Read the lizard description as it stands in the wiki, in a row, and then their creeds description right after, and read tanora's description before or at the same time, and you'll see what i mean.