what is the tense of that sentence?

Non-past: the final verb ends in ます. But we are talking about the tense of adjectives, not sentences. Re-read the topic of this thread: "Progressive form for 好き and 嫌い" not "Progressive form for verbs."

There is no progressive form for adjectives. Period. This is not up for debate. It is a fact.

"好きでいます and 好きしています - which of them two is the correct progressive form?" is original question by thread maker.
What's wrong with talking about tense of "好きでいます”？
Thank you so much.

Look at the title of the thread. "Progresive form for 好き and 嫌い. When OP talks about the progressive form, he's asking for the progressive form of an adjective. I'm merely pointing out it is literally a nonsense question.

It's like saying "Can someone explain to me what the color of a dog's bark is?"

I thought that fairly explicitly answered OP's question. But if you insist on me spelling it out further, neither of OP's sentences is the correct progressive form of 好き. This is because there is no such thing. It may be a grammatically correct sentence, but that's not the question being asked by OP!