This is probably a stretch but it somehow fits.

Woman who likes to slice things up?

Because

She 'saw' herself out.

(Not meant to hurt any social, religious and/or political sentiment)

Is it an

Israeli Jew?

"I like baseball", says a man.

On this website, Iraq is ranked 6th in regional popularity of baseball around the world.

"I prefer hiking", answers a woman.

In order to hike, you need a navigable route i.e. mountain pass. The
Zagros mountain ranges of Iraq have these in plenty.

"I love persian culture", tells a second man.

The large number of Shia Muslim population means a shared culture with Iran (i.e. Persia).

"It's weird, but I like to slice things up", says another woman.

Due to the large Muslim population, this may refer to slicing of meat
and beef as per Halal conventions.

"As for me, I really enjoy eating in the evening", tells the last man.

This probably refers to iftar
during the Ramadan fast.

"Well, I guess I'm not welcome here, so I'll see myself out."

Why?

From the above, it is clear that the above group is that of Shia Muslims
living in Iraq. Now, where might these people be living in? A place in
Iraq where there is local diversity. What better palce than Baghdad
may fit this criteria. The Israeli Jew may feel that the group is unsafe
and leave it on account of March 1950 Denaturalisation Act and 1950–1951 Baghdad bombings, wherein
hundred thousand of Iraqi Jews were targets of a series of bombings in Baghdad.

Person who likes Baseball cannot play alone.The one who prefers hiking can go to hiking alone. The one who loves Persian culture can read about them alone.The one who loves to slice things up can slice some vegetables or fruits and cook something for the person who loves to eat. So there's no one to play with the baseball guy.

This may be far too simple, but is it

The second man (the fan of Persian culture)?

The reason being that...

Everyone enjoys an action (including baseball, which despite being a noun involves sport/action), whereas the second man is simply a fan of a given culture.

Answer:

It is

The second man, who tells of loving Persian culture.

Why?

Because he is the only person out of the five people who does not relate to a card suit.

$$$$

Explanation:

"I like baseball," says a man.

1. 
   

   The first man loves baseball. In baseball, the field is in the shape of a diamond $to$ diamond cardsuit $diamondsuit$. He is a man because the infix "mon" in the word, diamond, sounds like man.

   
   

"I prefer hiking," answers a woman.

2. 
   

   The first woman prefers hiking. In the very word, there is a mention of king $to$ the king in a deck of cards. She is a woman for she is queen to the king (because she loves $heartsuit$ hiking, a reference to the hearts card suit).

   
   

"I love Persian culture," tells a second man.

3. 
   

   The second man loves Persian culture $to$ no cards related. (Odd one out.)

   
   

"It's weird, but I like to slice things up," says another woman.

4. 
   

   The other woman likes to slice things up. You can use a spade to dig and/or slice things with its sharp edge $to$ a spade cardsuit $spadesuit$. (There are also many slicing card magic tricks.) She is a woman because when upside-down, the spade looks like a heart $requireHTML styledisplay: inline-block; transform: rotate(180deg)spadesuit$, another card suit $heartsuit$. Or, she being a woman might (additionally) be referencing Kate Spade who was a fashion designer (and recently passed away by suicide, how tragic).

   
   

"As for me, I really enjoy eating in the evening," tells the last man.

5. 
   

   The last man enjoys eating in the evening. This hobby has nearly all words starting with e (enjoys eating in the evening), which is the suffix of the word tree (and sounds like the word, too, as well as the word, really, and me in "as for me") $to$ the clubs cardsuit that looks like a tree $clubsuit$. He is a man because the sport golf is mostly played by men, a reference to golf clubs (and he might be using a dining gift card!).

   
   

After a brief pause, one of them finally says:
"Well, I guess I'm not welcome here, so I'll see myself out."

i.e. the second man.

Granted this is a long shot, but is it:

The woman who likes to slice things up?

Reason being:

You say she's "another woman", which is a colloquial term for "mistress". When she says that she likes to "slice things up", the other people could understand the "thing" to be a marriage or other relationship, and this comment could be seen as being in very poor taste.

Is it:

The man who likes eating at evening.

Because:

He interjects himself into a conversation with the two couples and wasn't originally a part of the conversation in the first place.