I believe the question by itself cannot be answered because immigration policy, welfare policy, and public safety are all intricately linked.

For example, I think people would be much more open to free immigration if they weren't receiving welfare benefits and if local law enforcement was sufficient to prevent any increased risk of crime.

On the other hand, when taxpayer funded welfare benefits are going to these immigrants who haven't paid into the system and when and if immigration contributes to crime, then people will want a tightened immigration policy.

But to me, I think the average westerner devalues their own culture too much. I speak as someone of Asian descent and thus having no historical ties to western culture: It would be really sad to me if Germany or France one day became a muslim-majority country. Not because I hate muslims, but because I think something of value would have been lost: a unique German or French cultural identity that had persisted for many thousands of years but now can no longer be seen.

Of course, cultures are always undergoing flux so this argument isn't definitive. Nevertheless, because I think the average westerner devalues their own culture too much, I would generally support more restrictive immigration policies in western countries. In that sense, while I don't know what the optimal immigration policy is, the first derivative points me towards more restrictions in western countries.