It isn't clear to me exactly what the tension is. It will, no doubt, depend on the religion in question. Some religions do not hold that the non-believer will be punished or that there is a special religious basis for morality. In my experience, many who do believe that the non-believer will go to hell make an effort to "save" souls; those who don't may be shy or preoccupied with other things. Being uninterested in converting others is not the same as being opposed to it (though more on this below).

On the broader issue of morality, I'm not sure why the religious person is in a position any different from any moral person. If believe that eating meat is morally wrong (for whatever reason), should I try to convince others to become vegetarian? Well, one's answer will depend on the broader moral theory one subscribes to. If I'm a utilitarian, I'll have to determine whether trying to convince others to be vegetarian will have the best consequences; maybe I'm terrible at such efforts and could better spend my time in other morally worthwhile projects. If I believe that eating meat is wrong because God says so, and my view of morality is that one ought to do what God says, then whether I should try to convince others to be vegetarian will depend on whether God tells me to. There's no inconsistency in believing that God says that I should be vegetarian and also says that I should not attempt to convert others to vegetarianism (maybe God wants this job for him/herself).

But maybe you are wondering how the belief that an action is wrong is compatible with tolerating someone's performing the action. Toleration is a complicated and difficult concept. But it might help to start with the thought that tolerating or not tolerating something is itself an action. Some moral views have strong principles of non-interference, so there may be difficult trade-offs when such a principle comes into conflict with another substantive principle. Usually talking or reasoning with others is not considered interference, so there's plenty of room to try to talk people out of doing wrong. But in the spiritual domain there is sometimes the idea that we must each walk our own spiritual path and do our own spiritual work. So this vague idea may be behind some hesitation within religious contexts to put any pressure on others to conform on matters of faith. This also raises questions about the nature of faith and the differences between faith and reason (how does conversion really happen?).