May I know what does this sentence in English mean?

Muslims and non- Muslims who are otherwise similar with regard to the remaining independent vari- ables in the models.

Thank you very much

That is not a sentence. There is no verb.

“Independent variables in the models” must refer to some scientific / sociological model that uses multiple variables to define something. Those may be certain characteristics or social constructs – it is impossible to tell from this small bit.

“Independent variables” can be characteristics or bits of data that have no relation to each other. For example, skin color and intelligence are independent variables – they are unrelated. On the other hand, intelligence and proper nutrition in early childhood are dependent variables – one has an influence on the other. In a population where skin color and intelligence appear to correlate, there must be another dependent variable, such as nutrition, that explains the illusion of a link between the unrelated variables. (I apologize if the level of language I used here is inappropriate for a learner!)

The author seems to want to highlight some contrast between Muslims and non-Muslims. The “who are otherwise similar” phrase indicates that they are alike in some ways which are defined by those unnamed variables, but the “otherwise” hints that he is about to show how they are not alike in some way.

There is no main* verb.
I’m sorry but your examples are not technically correct.
In statistics and experimental design an “independent variable” is a variable, a factor, that you manipulate or select so as to test its effect on other variables. This second set of variables (that may be affected, influenced by the independent variables) are called “dependent variables”.
In your example, intelligence would be a dependent variable and both skin color and nutrition would be independent ones, whether they have an effect on intelligence or not! because the research would have (for example) selected groups of people based on their color skin and also according to their nutrition habits (or, alternatively, you would have told them to follow a particular diet for some time), so the researcher would have decided the levels of those two variables, which is what defines a variable as “independent” then (s)he would have measured the level of intelligence to test if the two independent variables have any effect on intelligence (this measurement of intelligence is what defines it as a “dependent variable”). Quite probably the researcher would discover that (as you say) nutrition has an effect whether, whereas skin color would not, but that would not change the status of either as independent variables or of intelligence as a dependent one.

The sentence means something like this:

Possible background:
The authors have proposed a statistical model that relates some sociological variables (“independent variables”) to predict other variables (“dependent variables”). For example maybe they predicted the effect of income, education level, faith, gender, (independent variables) on the tendency to vote for one or another political party (dependent variable).
In their discussion, they come to consider to what extent the independent variables correlate between themeselves (this is important for several statistical models, such as linear regression)

Meaning of the sentence:
They say that the independent variable “faith” (which compare Muslims to non-muslims) does not change with resepct to the rest of independent variables of the model. For example, that muslims and non-muslims are not different in average in education level, …

It’s pretty technical but I hope it’s a bit clearer now

May I know what does this sentence in English mean? (incorrect)
What does this mean? (correct)
Explain this to me, please.(correct)

There exist two or more models.
Each of the models involves people.
The people are not identical to each other but they are the same for all of the independent variables, except for the variable of religion.
Regarding religion, some of the people are Muslim and some are non-Muslim. In other words each person in all of the models is either Muslim or non-Muslim.

I hope that helps you understand this. → Muslims and non- Muslims who are otherwise similar with regard to the remaining independent vari- ables in the models