A lot of the answers here deal with the first part of this, but not much about the 2nd part of the question, so I thought I'd jump in, here:
The first part: Saying "Congress shall make no law respecting an establishment of religion" means they can't establish an official religion, and that is why it is known as the Establishment Clause. This was addressed pretty well in other posts.
The second part:
Doesn't "Congress shall make no law respecting an establishment of religion" mean congress should not make a law that respects religion because there's "no" in it??
This seems, to me, to be asking:
- Why it is that Congress can allow people to worship at a church at all?
- Why it is that religion is even allowed to exist, legally?
- Why it is that, if a person is religious, laws were allowed to be written to protect them (from being discriminated against, for example).
In other words, why is religion protected, if Congress can't pass laws "respecting" it (which here, can be read with either definition for "respecting" I give below)?
Well, others did clarify the definition of respecting, that it means "concerning", here - not "in honor or reverence of" - but the key word in the sentence is "establishment", not "respecting", here, because, as I said, you could put either of those definitions in that last sentence and it still makes for a good question. The previous answers given didn't specifically say that "establishment" was the key word - they honed in on "respecting" and mentioned it was the "Establishment Clause", but didn't say anything about the reason why laws that "respect" ("honor" or "concern") religion are legal. And fortunately, regardless of which meaning you use, there's a single answer: Yes, Congress can't establish a religion, but the 14th Amendment says everyone deserves "equal protection under the law", regardless of a religious belief, gender, race, etc. This is what makes Congress have to "respect" (read "honor") a person's religion, and why those laws that do so are legal, and in fact, are just re-affirmations of the 14th Amendment.
And I didn't realize this until I did some more research, but there's actually some controversy as far as how far the 14th Amendment's equal protection clause goes to protect religion, identified in this good, scholarly, and well-researched report from Northwestern University:
In that report, they call attention to the fact that apparently some cases have been decided (incorrectly, they assert) on the difference of how many rights religious people had in 1868 (when the 14th Amendment was passed) vs. those rights of people in other discrimination lawsuits that weren't identified by the court until after 1868, as to who has more credibility to say they were discriminated vs. who has not been. They claim the 14th Amendment protects those in the religious class just as equally as those in a gender or racial one.
And they bring up the Blaine Amendment issues, where a state typically has a constitutional amendment in their state constitution that can be read so as to deny funding to private schools based on that school being a religious one, in order to avoid the appearance of the state establishing a religion, which seems to acknowledge that the 1st Amendment has precedence over the 14th when it comes to a possible perception by someone of the government's establishment of a religion. It may help to understand where some of the legal precedents have come from, with respect to why, legally, laws are written to generally uphold (respect/honor) religious practices, so long as they do not mean the government can be perceived as establishing them.
More about the Blaine Amendment: http://education.findlaw.com/curriculum-standards-school-funding/what-is-a-blaine-amendment.html