2. Accept Righteous Gentiles

This requirement says that you must be willing to accept righteous gentiles.  Righteous gentiles are moral non-Jews using whatever moral standards your Judaism specifies.  Talmudic Judaism defines this as Noahides.  The Torah defined this as the foreigners in Israel who accepted living under Torah law.  And Biblic Judaism has its own standard.  To accept means not to reject.  In particular, this means accepting righteous gentiles in synagogue with roughly equal treatment given Jews.

What does the Torah say about foreigners?

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You also must love the foreigner, since you were foreigners in the land of Egypt.
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Deuteronomy 10:19

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“When a foreigner lives with you in your land, you must not oppress him.  You must regard the foreigner who lives with you as the native-born among you. You are to love him as yourself, for you were foreigners in the land of Egypt; I am Yahweh your God.
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Leviticus 19:33-34

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The assembly is to have the same statute for both you and the foreign resident as a permanent statute throughout your generations. You and the foreigner will be alike before the Lord. The same law and the same ordinance will apply to both you and the foreigner who resides with you.”
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Numbers 15:15-16

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“If a foreigner resides with you and wants to observe the Passover to the Lord, he is to do so according to the Passover statute and its ordinances. You are to apply the same statute to both the foreign resident and the native of the land.”
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Numbers 9:14

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Rejoice before Yahweh your God in the place where He chooses to have His name dwell—you, your son and daughter, your male and female slave, the Levite within your gates, as well as the foreigner, the fatherless, and the widow among you.
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Deuteronomy 16:11

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“Say to them: Anyone from the house of Israel or from the foreigners who live among them who offers a burnt offering or a sacrifice but does not bring it to the entrance to the tent of meeting to sacrifice it to the Lord, that person must be cut off from his people.
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Leviticus 17:8-9

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Moses wrote down this law and gave it to the priests, the sons of Levi, who carried the ark of the Lord’s covenant, and to all the elders of Israel. Moses commanded them, “At the end of every seven years, at the appointed time in the year of debt cancellation, during the Festival of Booths, when all Israel assembles in the presence of the Lord your God at the place He chooses, you are to read this law aloud before all Israel. Gather the people—men, women, children, and foreigners living within your gates—so that they may listen and learn to fear the Lord your God and be careful to follow all the words of this law. Then their children who do not know the law will listen and learn to fear the Lord your God as long as you live in the land you are crossing the Jordan to possess.”
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Deuteronomy 31:9-13

When King Solomon built the first temple, he said:

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Even for the foreigner who is not of Your people Israel
but has come from a distant land
because of Your name—
for they will hear of Your great name,
mighty hand, and outstretched arm,
and will come and pray toward this temple—
may You hear in heaven, Your dwelling place,
and do according to all the foreigner asks You for.
Then all the people on earth will know Your name,
to fear You as Your people Israel do
and know that this temple I have built
is called by Your name.
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1 Kings 8:41-43

And in fact, to my knowledge, foreigners (non-Jews) with a genuine desire to worship God were never turned away from any of the three temples of Israel.  What does God say about these foreigners?

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No foreigner who has joined himself to the Lord
should say,
“The Lord will exclude me from His people”;
and the eunuch should not say,
“Look, I am a dried-up tree.”
For the Lord says this:
“For the eunuchs who keep My Sabbaths,
and choose what pleases Me,
and hold firmly to My covenant,
I will give them, in My house and within My walls,
a memorial and a name
better than sons and daughters.
I will give each of them an everlasting name
that will never be cut off.
And the foreigners who join themselves to the Lord
minister to Him, love the name of Yahweh
and become His servants,
all who keep the Sabbath without desecrating it
and who hold firmly to My covenant—
I will bring them to My holy mountain
and let them rejoice in My house of prayer.
Their burnt offerings and sacrifices
will be acceptable on My altar,
for My house will be called a house of prayer
for all nations.”
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Isaiah 56:3-7

The concept in the Hebrew Bible is clear.  God wants Jews to welcome foreigners and allow foreigners to learn Torah.  In fact God clearly states the purpose of Judaism.

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“I, Yahweh, have called You
for a righteous purpose,
and I will hold You by Your hand.
I will keep You and appoint You
to be a covenant for the people
and a light to the nations,
in order to open blind eyes,
to bring out prisoners from the dungeon,
and those sitting in darkness from the prison house.
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Isaiah 42:6-7

How exactly can Judaism be "a light to the nations" if non-Jews are excluded from synagogues?

Clearly any rabbi who turns away non-Jews from synagogue is violating the Torah, and therefore we should not consider this rabbi as a Jew.  He is simply a racist, no different from a Nazi.

Jews have an obligation to accept all moral people whether those people are Jewish or not.